If I was God. I.

I have tried to skiss out a picture of emerging Life and I will continue from the Creators wiev. How would I do it if I was God?

Living matter is different from non-living in a number of ways:
1. Open entropic systems, that means the mass is relative and changeable. Form and structure as topology, fractality and hierarchy are relatively stable? Superconduction and solitons are used?
2. Negentropy is selected for, in terms of information. What exactly describes that information? Patterns, densities, but also meanings, new creation of patterns that are pure mathemathical? Negentropy is conserved and renewed or recombined, conserved in DNA and memory (as a chrystal phase?), recombined in mutations, learnings and adaption.
3. Complexity and networkings, signalling near and far away. See pt. 5.
4. Self-organization, healing and regeneration, differentation.
5. Growing, regeneration of a self, selfreplication as new individuals (reproduction), propagation, , spreading of the negentropy.
6. Adaption, change, mutation.

Negentropy is in the zero point? Quantum world? The Dirac Sea, QCD vacuum? Life is quantal?

If I was God I would certainly look very close on this A-phase of matter to see if it could be used to create Life, forms and structures?

Sanda: "I do not think that all these conditions have been chosen randomly. I suspect that the Mother Nature has gone out of Her way to show us CP violation, and She is also showing us the way to the fundamental theory." in The Road to the Discovery of Large CP Violation in B Decays. A Miracle Story.


Three ways to look.
1. From our wiev: The models of Universe can either begin with the electronuclear force symmetry as fundamental property that then will be broken (GUT, with no gravity, top-bottom) Or as a reductionistic wiev with ever smaller parts from the bigger ones (a deeper understanding is gained by dividing things into smaller parts)
2. From Big Bang wiev: with anti-GUT where symmetry is gradually built in and created (bottom-up) An emergent wiev (particle-wave duality -> origin of particles = origin of waves).
Superstring theory as opposed to condensed matter theory, acc. to Wen. Different organizations (orders, phases) of particles leads to different kinds of waves and wave equations. Different organizations -> different waves -> different kinds of particles.
Originate from organization = principle of emergence.
3. The holistic approach is the third way. Holism= can be seen in every part too. Creation. Environment is important. Holism is the fundamental union? This is the Creators wiev?

I think this is important to keep in mind.


First some basics.
CP symmetry (charge conjugation and parity symmetry) states that the laws of physics should be the same if a particle were interchanged with its antiparticle and left and right were swapped (incl. time). The strong interaction and electromagnetic interaction seem to be invariant together under the combined CP transformation operation, but not during certain types of weak decay. Weak interactions violate the P symmetry or, as the analogy goes, some reactions did not occur as often as their mirror image. Asymmetry is born.

Addition: Parity is also violated now by strong interaction (Taylor Muzzin)? The physicist is still quick to point out that the effect only suggests parity violation - it doesn't prove it. If the effect proves to be real, it could help scientists understand a similar asymmetry that led to one of physics' most fundamental mysteries - namely, why the universe is dominated by ordinary matter today.

Parity was long thought to be a fundamental law of nature. It essentially states that the universe is neither right- nor left-handed — that the laws of physics remain unchanged when expressed in inverted coordinates. In the early 1950s it was found that the so-called weak force, which is responsible for nuclear radioactivity, breaks the parity law. However, the strong force, which holds together subatomic particles, was thought to adhere to the law of parity, at least under normal circumstances. Now this law appears to have been broken by a team of about a dozen particle physicists, including Jack Sandweiss, Yale’s Donner Professor of Physics. Since 2000, Sandweiss has been smashing the nuclei of gold atoms together as part of the STAR experiment at RHIC. The plasma “bubble” created in the collisions at RHIC lasted for a mere millionth of a billionth of a billionth of a second, yet the team hopes to use it to learn more about how structure in the universe — from black holes to galaxies — may have formed out of the soup. Parity violation is very difficult to detect, but the magnetic field in conjunction with parity violation gave rise to a secondary effect that we could detect.

And in Physical Review Letters/RHIC/Science Daily, II, Physicists have predicted an increasing probability of finding such bubbles, or local regions, of "broken" symmetry at extreme temperatures near transitions from one phase of matter to another. According to the predictions, the matter inside these bubbles would exhibit different symmetries - or behavior under certain simple transformations of space, time, and particle types - than the surrounding matter.

Schematic QCD phase diagram for nuclear matter. The solid lines show the phase boundaries for the indicated phases. The solid circle depicts the critical point. Possible trajectories for systems created in the QGP phase at different accelerator facilities are also shown.


The CP violation (Nobel prize 1980, 2008) discovery once shocked particle physics and opened up questions still at the core of particle physics and cosmology. The lack of an exact CP symmetry, but also the fact that it is so nearly a symmetry, created a great puzzle. A weaker variant, the CPT symmetry (T=time, reversal of motion in time) came up, but a violation of the CP symmetry is equivalent to a violation of the T symmetry.

There are also other symmetries. Geometric symmetries, permutation symmetries, space-time symmetries, gauge symmetries... R-symmetry, dynamical symmetries based on vibrational and rotational symmetries etc. Algebraic and other mathematical structures are at the basement.


To create the required imbalance in matter and antimatter, because our Universe is made of matter, (asymmetry, chirality, no antimatter) out of an initial condition of balance, the Sakharov conditions must be satisfied, one of which is the existence of CP violation during the extreme conditions of the first seconds after the Big Bang (the violation of CP symmetry is a necessary condition for baryogenesis, the process thought to be responsible for the matter-antimatter asymmetry of the universe.) Also creation of magnetic monopoles did happen then? The laws of physics distinguish between matter and antimatter.

The Big Bang should have produced equal amounts of matter and antimatter if CP symmetry was preserved with total cancellation (annihilation) of both- protons should have cancelled with antiprotons, electrons with antielectrons, neutrons with antineutrons, and so on for all elementary particles. This would have resulted in a sea of radiation in the universe with no matter. Since this is not the case, after the Big Bang, physical laws must have acted differently for matter and antimatter, i.e. violating CP symmetry. - The 4% difference is fundamental in the chirality? (TGD-diary, A new dark matter anomaly, 1.10, 2009.). Today this is debated in the neutrino- antineutrino oscillation results.

But this statement also means the cancellation creates dark energy, the sea of radiation, for the other 96%?

Explanations which do not involve CP violation are less plausible, since they rely on the assumption that the matter–antimatter imbalance was present (implicitly?) at the beginning, or on other admittedly exotic assumptions.

The other Sakharov conditions were the stability of proton (baryon) and that the cosmos originated in the heat of the Big Bang (equilibrium violated).

So we get a polarity here between the symmetry and the stability and the product is matter.

The true ground state of the quarks is quite different from the naive fermi balls. It is characterized by the formation of a coherent condensate, and the development of an energy gap. The condensation, which is energetically favorable, is inconsistent with a magnetic field, and so weak magnetic fields are expelled. This is the famous Meissner effect in superconductivity, which is essentially identical to what is known as the Higgs phenomenon in particle physics. Wilchek 1999.

Quantum Field Theory, reductionistic wiev, explains nature's electromagnetic, weak and strong nuclear forces (though not gravity). The boson/fermion dichotomy is mandated by the Spin-Statistics Theorem of QFT. Elementary particles are classified into bosons and fermions (anyons, are neither). The distinction is made on the basis of the symmetry of their wavefunction upon particle exchange. As the identical particles are indistinguishable, exchange of two particles changes the wavefunction at most by a factor C. The choice of the sign of C is intimately linked to the spin quantum number of the particles, namely, particles having an integer spin quantum number take C = +1 and are called bosons, whereas those with a half-odd spin take C = −1 and are called fermions. Doing the two-particle exchange twice brings the system back to the original situation, so that C² = 1, and hence C = ±1.

Bosons can pile on top of one another without limit (superposition), all occupying the same quantum state. Why? The phi-state? The infinities, polarities? At low temperatures (low entropy), this causes phenomena as superconductivity, superfluidity and Bose-Einstein condensation. It also allows photons of the same frequency to form coherent laser beams.
Fermions, on the other hand, avoid one another. Electrons around a nucleus stack into shells (octonions) instead of collapsing into a condensed cloud, giving rise to atoms with a great range of chemical properties. Thus the nucleus determine the electron charachter. Unity is bosonic, differentiation is fermionic.

Bosons, which are governed by Bose-Einstein statistics, are particles/waves with an intrinsic integer spin of 0, 1, 2 or other integer, and include photons, W and Z bosons, and gluons. They are often force carrier particles. Bosons may be either elementary, like photons, or composite, like mesons, some are not truly bosons (e.g. helium-4 atoms); a more accurate term for such composite particles would be "bosonic-composites", and are important in superfluidity and other applications of Bose–Einstein condensates. A composite particle containing an even number of fermions is a boson, since it has integer spin. As instance, the nucleus of a carbon-12 atom contains 6 protons and 6 neutrons (all fermions) and is therefore a boson; The spin is the important thing.

• Photons are the force carriers of the electromagnetic field.
• W and Z bosons are the force carriers which mediate the weak nuclear force (seen 1983) can get mass; the charged vector boson W+/- carries a superposition of weak and electromagnetic charges, whereas the neutral vector boson Z0 carries only the weak isospin charge. The W boson can have a positive or negative charge (+1 or -1), and the Z boson is electrically neutral. Z bosons can only transfer momentum, and their interactions are therefore called neutral current interactions..
  
• Gluons are the fundamental force carriers underlying the strong nuclear force, and they have a spin of +1. There are eight distinct gluons (colors), each their own antiparticle. No free state gluons have been observed.
• X and Y bosons may or may not exist, it is presumed that they would allow for a new force which would bind particles called leptons (as electrons) to particles called quarks (as protons).
• All particles have a sort of angular momentum which is labeled spin. This spin gives the magnetic properties. Some say the Higgs particle is spinless (an anyon?). Charges are often called the coupling constants because their strength determines the coupling, or interaction strength with the corresponding fields.
  

The standard model postulates the existence of Higgs bosons, which give other particles their mass via the Higgs mechanism. After symmetry breaking, three of the four degrees of freedom in the Higgs field mix with the W and Z bosons (naturally massless), that get mass, while the one remaining degree of freedom becomes the Higgs boson – a new scalar particle, and its own antiparticle (a quasiparticle?). Other numbers of possible Higgs bosons are also calculated, and other Higgs mechanisms. In QCD, condensed matter physics, it is the gluon that get mass. So the options is between the weak and the strong forces. Notice there are no virtual charges without virtual mass.

Fermions, governed by Fermi-Dirac statistics, are all particles with odd-half-integer spins – ½, 3/2, 5/2, etc. – and include the electron, neutrinos, muons and all the quarks = the fundamental particles that make up protons and neutrons. Fermions are usually associated with matter, although Majorana and massless Weylfermions is also. Only one fermion can occupy a quantum state at a given time (Pauli exclusion princip). This results in "rigidity" or "stiffness" of states (atomic nuclei, shells, atoms, molecules, etc.).

There are two types of elementary fermions: quarks and leptons. In total, there are 24 different fermions: being 6 quarks and 6 leptons, each with a corresponding antiparticle:

• 12 quarks - 6 particles (u · d · s · c · b · t) with 6 corresponding antiparticles (u · d · s · c · b · t)

• 12 leptons - 6 particles (e⁻ · μ⁻ · τ⁻ · ν_e · ν_μ · ν_τ) with 6 corresponding antiparticles (e⁺ · μ⁺ · τ⁺ · ν_e · ν_μ · ν_τ)

Composite fermions, such as protons and neutrons (hadrons) are essential building blocks of matter. Weakly interacting fermions can also display bosonic behaviour, as in superconductivity. The known fermions of left-handed helicity experience weak interactions while the known right-handed fermions do not. Or put another way, only left-handed fermions and right-handed antifermions interact with the W boson.

• A baryon, such as the proton or neutron, contains three fermionic quarks and is therefore a fermion;
• The nucleus of a carbon-13 atom contains 6 protons and 7 neutrons and is therefore a fermion;
• The atom helium-3 (³He) is made of 2 protons, a neutron and 2 electrons and is therefore a fermion.

Life is very much bosonic. But Life doesn't act in low temperatures to eliminate the entropy because Life needs re-actions. Instead Life creates negentropy, or select it from the bosonic world. Coherence? Negentropic oscillations? Life is creative, interacting.


Interactions.
Bosons never become fermions?
Composite particles: Electrons having spin ½ are fermions. In our three-dimensional(3D) world, the distinction between fermions and bosons is strictly enforced. In a two-dimensional (2D) world, however, the rule can be relaxed by a trick called flux attachment. One can transform a fermion to a boson (or vice versa) by attaching to it fictitious magnetic flux(es), which takes care of the change in the phase of its wavefunction. No transformation of the exchange path is possible in 2-D, but in 3-d, yes. In surfaces, not spheres.
Elementary particles: Bosons play by one set of rules while fermions, including electrons, play by another. Do bosons ever play by fermion rules? Specifically, do photons act like bosons all the time, or could they sometimes act like fermions? The answer is a solid "no."

So, there can be no bosonic 'emergence' into matter at particle level. Bosons can never be massive particles (only W- and Z bosons slightly)? Like photons they can only interact by giving energy as a power of time (light speed). They are gauge bosons. Energy is bosonic? The energy content is not dependent on matter either. At the end everything is energy. Everything is controlled by forces, but emergent quantal properties is made manifest only through composite bosons.

Matter is no 'condensation' of energy? Matter is a relaxation of energy from a superpositional quantal bosonic state, coming from the CP(T)-violation? Like a phase shift. And Life has very much more narrow constrictions than ordinary matter. Like a phase in a phase.

The electric force depends only on charge (bosonic; in fields=mediators) and not on the particular nature of particles. For example, the electric force between two muons, which are particles with the same charge as the electron but 200 times heavier, is equal to that between two electrons in the same external conditions. Since our physical world has 3-D, electric and magnetic fields are 3-component vectors defined at every point in space. Equivalently, the fields are vector-valued functions of space. A point-like particle with positive (negative) electric charge has an electric field radially pointing outwards (inwards). Electric charges are also responders to the electric field, but neutrons have no field (neutral) and no respons.

Electrons can also be fractionalized and still have the same charge? What about ions then? The ion theory is not true? The ion is magnetic mostly? What is the electricity? Like photons it can travel, it is invisible, it responds to other charges. The mass can vary, but the charachter is the same. The time factor is excluded in this reasoning. Time is important too. What is time? Travelling and motions are time.

The fractional quantum Hall effect (FQHE) is a physical phenomenon in which a certain system behaves as if it were composed of particles with charge smaller than the elementary charge. Seen 1982, Nobel prize 1998. The effect is a manifestation of simple collective behaviour in a 2-D system of strongly interacting electrons. At particular magnetic fields, the electron gas condenses into a remarkable state with liquid-like properties. The electron can get bosonic properties in certain conditions. Is the electron a true fermion?

Electrons can be composite and chiral? What do that? Vortices?
An electron accompanied by an odd number of fluxes can be regarded as a composite boson. Therefore, the ν = 1 and ν = 1/3 QHE states can be viewed as a composite boson gas in zero magnetic field, and the QHE states can be interpreted as superfluid states of those composite bosons.

It is the magnetism that keeps the electron as a particle. The nucleus decide? The parity? An open parity (broken symmetry) gives a different spin and an ion? Broken symmetries are energetically instabile in that context.

The fundamental building blocks of the fractional quantum Hall effect are also composite fermions, which are electrons with an even number of quantized vortices attached to them. An even number flux quanta are captured by each electron, forming integer-charged quasiparticles. This makes electrons at a filling factor 1/3, for example, behave in the same way as at filling factor 1. A remarkable result is that the filling factor 1/2 corresponds to zero magnetic field for composite fermions, resulting in their Fermi sea.

Fractionally charged quasiparticles are neither bosons nor fermions and exhibit anyonic statistics. The fractional quantum Hall effect continues to be influential in theories about topological order.


Strong force - nuclear force - electric and magnetic dipole - gravity.
But neutrons bear the strong gluon force, 100 times the EM-force, and a 'field of gauge bosons'= gluon field, but are neutral? This force is not electric and weak, not gravitional. It is 'color' in the quarks. It is magnetic but without electricity. An anomalous magnetism? In the nucleus they are stable but not as free nucleons or neutronium, that's why they determine the isotopes and go through beta-decay. The only possible decay mode without a change of baryon number is for one of the quarks to change flavour via the weak interaction. The neutron consists of two down quarks with charge −¹⁄₃ e and one up quark with charge +²⁄₃ e, and the decay of one of the down quarks into a lighter up quark can be achieved by the emission of a W boson. By this means the neutron decays into a proton (which contains one down and two up quarks), an electron, and an electron antineutrino. Inside a nucleus, protons can also transform into a neutron via inverse beta decay. This transformation occurs by emission of a antielectron (also called positron) and a neutrino. The small and inhomogenous magnetic moment is an indication of substructure, i.e. that the neutron is made of other, electrically charged quarks.

Diagram of a strong proton-neutron interaction with the individual quark constituents shown, to illustrate how the fundamental strong interaction gives rise to the nuclear force. Straight lines are quarks, while multi-colored loops are gluons (the carriers of the fundamental force). Time proceeds from left to right. A neutral pion in middle. Wikipedia.

Decay is balanced against the instability of repulsive protons in bound states in nuclei. Also protons, which are stable in empty space, may transform into neutrons when bound inside of a nucleus. More neutrons are required in atoms with large numbers of protons.

Interaction through gravity, weak force. The neutron is an electric dipole with a magnetic moment and no net electricity. A tiny separation of positive and negative charge within the neutron leading to a permanent electric dipole moment.

Nuclear force:

Since nucleons have no color charge, the nuclear force does not directly involve the force carriers of quantum chromodynamics, the gluons. However, just as electrically neutral atoms (each composed of cancelling charges) attract each other via the second-order effects of electrical polarization, via the van der Waals forces (London forces), so by analogy, "color-neutral" nucleons may attract each other by a type of polarization which allows some basically gluon-mediated effects to be carried from one color-neutral nucleon to another, via the virtual mesons which transmit the forces, and which themselves are held together by virtual gluons. It is this van der Waals-like nature which is responsible for the term "residual" in the term "residual strong force."

Such systems can be described by attributing a potential (such as the Yukawa potential) to the nucleons and using the potentials in a Schrödinger equation. The form of the potential is derived phenomenologically. Nuclear interactions from the basic interactions in many-body systems are difficult to calculate. In particular, chiral symmetry breaking can be analysed in terms of an effective field theory (called chiral perturbation theory) which allows perturbative calculations of the interactions between nucleons with pions as exchange particles. The pion decay constant may be viewed as a measure of the magnitude of the chiral symmetry breaking.

No wonder physicians avoid bond states, but Life is about complexity. How could these immense degrees of freedom be fixed? Only through entanglement (bosonic state) into bigger bits, qubits. These are made topologically in a fractal way. If I was God I would try that way.

W-boson electric dipole... known leptons and quarks are not elemental but topological condensates. Heavy leptons and quarks are excited states with spin 1/2, 3/2 etc. with the same quantum numbers as the existing fermions. Interactions between ordinary and heavy fermions tend to be of magnetic type, mediated by gauge bosons. The chirality means that the interaction is only to lefthanded, and the interaction with electrons are about 0,5 when one handedness is left out.

Photons (gives electromagnetism) without mass travel with the same velocity in spite of different energylevels. As do nerve pulses. Mass-independence. And thence also gravity-independence? See the Michelson-Morley experiment. Gravity's main aspect is attraction, and it is felt and influenced by all energy, everywhere. Even light loses energy in the gravitational field of a massive body, as in black holes. The graviton is thought to be responsible for gravity, or gravity is emergent through mass. Magnetism can generate gravity, says Jerry Decker. How? We look at that later. It would be natural if gravity would be emergent, when it has no room in QFT.

Can fermions act as bosons?
Only as composites. But this matter as wave-function? What is it then? Neutral (iniert) particles and fields - and gravity? The interaction happens at the bosonic composite level? In 2-D but not in 3-D? The complexity has always been seen as an obstacle. Gravity is a surface-entanglement problem?


Complexity - relaxation in bound states. And 'emergence' of new dimensions? A topological paradigm?
If I was God and tried this puzzle, I would try to lay one piece upon the other and make them fuse. Then I needed only the basic degrees of freedom? It would be much more simple? Bosonic states of matter would be interesting. Like carbon. Maybe I could use carbon?

Fermionic or bosonic behavior of a composite particle/system is only seen at large (compared to size of the system) distance. At proximity, where spatial structure begins to be important, a composite particle (or system) behaves according to its constituent makeup. Fermions can exhibit bosonic behavior when they become loosely bound in pairs, as quasiparticles. This is the origin of superconductivity and the superfluidity of helium-3: in superconducting materials, electrons interact through the exchange of phonons, forming Cooper pairs, while in helium-3 (fermion), Cooper pairs are formed via spin fluctuations (paramagnetism).

Fractionally-charged quasiparticles based on accurate trial wave functions for the ground state at fraction 1 / q as well as its quasiparticle and quasihole excitations. The excitations have fractional charge. The FQH effect shows the limits of Landau's symmetry breaking theory. Previously it was long believed that the symmetry breaking theory could explain all the important concepts and essential properties of all forms of matter. Different FQH states all have the same symmetry and cannot be described by symmetry breaking theory. Thus FQH states represent new states of matter that contain a completely new kind of order—topological order. FQH liquids indicates that there is a whole new world beyond the paradigm of symmetry breaking, a basic topological paradigm, greatly enrich our understanding of quantum phases and quantum phase transitions. The associated fractional charge, fractional statistics, non-Abelian statistics, chiral edge states, etc demonstrate the power and the fascination of emergence in many-body systems.

This fractional charge tells also about hierarchy? The hierarchy of quantum Hall states is associated with a corresponding hierarchy of classical fluids. Results are given for the energy at many rational filling factors and for the pair-correlation function at ν=2/7.

There can be field configurations of bosons which are topologically twisted. These are coherent states (or solitons) which behave like a particle, and they can be fermionic even if all the elementary particles are bosons. Fermions made of bosons are named Skyrmions, and involves fields which take values on a 3-D sphere. In Skyrme's model, which is reproduced in the large N or string approximation to QCD, the proton and neutron are fermionic topological solitons of the pion field. In the chiral limit when the light quark masses mu,md,ms tend to zero, such that the octet of the pseudoscalar mesons π,K, η become nearly massless (pseudo) Goldstone bosons, they are the lightest degrees of freedom of QCD. The other three quark masses are heavy, tend to infinity.

- One very light, almost nothing, one very heavy? Like a quasiparticle?

The model is not good in small N. If the mean field happens to be small, the valence level is shallow, the Dirac sea is weakly distorted, and there are few antiquarks. In this case the model reproduces the well-known spin and space quark wave functions of the nonrelativistic models for baryons. If, on the contrary, the mean field happens to be very broad, the valence level dives towards the negative-energy Dirac sea, and there are O(Nc) (that is many!) additional Q¯Q pairs in a baryon, whose energy can be approximated by the two- and four-derivative Skyrme Lagrangian. The realistic picture is somewhere in between the two extremes.

Understanding the quark origin it becomes possible to formulate what is the Skyrmion in terms of quarks and demystify the famous prescription of the Skyrme model that a chiral soliton with a topological (or winding) number equal to unity, is in fact a fermion.The Skyrmion is nothing but the mean chiral field binding quarks in a baryon.


CKM-matrix, Kobayashi and Maskawa’s calculation matrix, contains probabilities for describing how the transformation of the quarks will take place. Found the solution in a 3 x 3 matrix in flavour-changing weak decays, as instance, the object that couples to the up quark via charged-current weak interaction is a superposition of down-type quarks. A rotational matrix is used. It turned out that the quarks and antiquarks swapped identity with each other within their own family. Quasiparticles - soliton? If this exchange of identity with double broken symmetry was to take place between matter and antimatter, a further quark family was needed in addition to the other two. Three is needed to get a CP-violation. Small hints is at a fourth generation too?

On the left is the weak interaction doublet partners of up-type quarks, and on the right is the CKM Matrix along with a vector of mass eigenstates of down-type quarks. The CKM matrix describes the probability of a transition from one quark i to another quark j. These transitions are proportional to |V_ij|².

The sum of all couplings of any of the up-type quarks to all the down-type quarks is the same for all generations. This relation is called weak universality. A rotational, mixing angle θ_c, now called the Cabibbo angle, between the d and s quarks resolve the second level. For the Standard Model case (N = 3), there are three mixing angles and one CP-violating complex phase. This requires a top quark?
For any fixed and different i and j, this is a constraint on three complex numbers, one for each k, which says that these numbers form the sides of a triangle in the complex plane. There are six choices of i and j (three independent), and hence six such triangles, each of which is called an unitary triangle. Their shapes can be very different, but they all have the same area, which can be related to the CP violating phase. The area vanishes for the specific parameters in the Standard Model for which there would be no CP violation. The orientation of the triangles depend on the phases of the quark fields. The total number of free variables independent of the choice of the phases of basis vectors is N² − (2N − 1) = (N − 1)². The masses and mixings of quarks have a common origin from the Yukawa interactions (potentials) with the Higgs condensate in SM. There are many possible parameterizations. The neutrino Koide triplet is the newest?

Sketch of the unitarity triangle. The six vanishing combinations can be represented as triangles in a complex plane, of which the ones obtained by taking scalar products of neighboring rows or columns are nearly degenerate.

Note: Some sort of deep physical asymmetry between up-type and down-type quarks maybe are, and thus CKM is not totally unitary. A small difference between inverse and conjugate transpose is possible. The first evidence is here for an anomalous CP violation in the mixing of neutral B mesons.

It should be possible to study a major violation of symmetry in B-meson particles, which are ten times heavier than their cousins, the kaons. Among other, the BaBar particle detectors is doing that. The first generation of CP violation experiments in the B-system, Belle and Babar at the B-factories, constrain the CKM matrix already considerably. The search for new physics beyond the Standard Model requires much larger statistics, combined with the study of other B-meson decays than those accessible at the B-factories. The aim is to exploit the copious production of all B-flavours at the LHC: ATLAS, CMS and LHCb.

While Skyrme's example involves pion physics, there is a much more familiar example in QED with a magnetic monopole. A bosonic monopole with the smallest possible magnetic charge and a bosonic version of the electron would form a fermionic dyon.

This is something geometric? Angles, form, structure? To me this resembles the code matrix in the genetic code. Also there are 24 'letters' (as the number of fermions). A code of materialization? Complex numbers consisting of a real and imaginary part and used in cubic equations containing the square roots of negative numbers, the theory of quaternions, complex Lie algebra, etc . A scale parameter is also present. Marni writes: It is not yet clear why conjugation on the $\pi /12$ should correspond to antineutrinos, but recall that conjugation is a standard feature of phases for antiparticles in the braid spectrum. The $2/9$ component appears to be shared by all particles, irrespective of their quantum numbers. Antimatter phase is rational multiples of $\pi$. ...in searching for new mass triplets.

Interesting. From the figure and other similar figtures one indeed sees how $\theta$ very near to $\pi /4$ is consistent with all measurements of neutrino oscillations if one allows mass scale to vary. In TGD model for CKM matrix in terms of topological mixing matrices U and D for U and type quarks (sphere, torus, and sphere with two handles characterizing the topology of partonic 2-surface associated with quark) the sum of mass squared for non-mixed quarks is integer if one uses p-adic mass squared scale as unit (and different for different quarks). This integer is not changed in mixing.

Integers: p-adics? Complex numbers: rational multiples of $\pi$.? Surfaces and spheres? Emergence of new dimensions? The same problem as in the genetic code.

What is the aim of mixing? Make the possible solutions as big as possible? The same as mutations in genetics?

Complex numbers are essential to spinors, which are a generalization of the tensors used in relativity. Twistors too. Pythagoras' theorem is wellknown.

Oscillations between matter and antimatter?
How does this double broken symmetry take place? Each kaon particle consists of a combination of a quark and an antiquark. The weak force makes them switch identities time and time again: the quark becomes an antiquark while the antiquark becomes a quark, thus transforming the kaon into its antikaon. Matter is just an oscillation. A kaon soliton between bosonic and fermionic states, between quantum world and real world? Between dense states and virtual states? Between matter and force. Fascinating!

Perturbative connectivity to a hypothetical liquid of noninteracting fermions ... as the interaction is slowly turned on from zero to its full strength, the original fermions turn into weakly interacting fermionic quasiparticles, but without a drastic reorganization of the low-energy Hilbert space or a phase transition. ... both (superconductivity and the fractional Hall effect) connect these exotic quantum liquids to certain ordinary Fermi liquids residing in unphysical Hilbert spaces... “(non) Fermi liquid” and “quasiparticles” are often used synonymously (hypothetical) By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid.

Density, pressure, space, time... gives quasiparticles?

Volovik (anti-GUT) (2008) in Emergent physics: Fermi-point scenario

That we survive in our Universe is not the result of the anthropic principle (the latter chooses universes that are fine-tuned for life but have an extremely low probability). On the contrary, this simply indicates that our Universe is also natural, and its vacuum is generic, though it belongs to a different universality class of vacua, the vacua with Fermi points. In such vacua, the masslessness of fermions is protected by topology (combined with symmetry). The mass is determined by the hierarchy of energy scales. Gravity emerges together with fermionic and bosonic matter; emergent fermionic matter consists of massless Weyl fermions; emergent bosonic matter consists of gauge fields.

Anyons that is neither fermions nor bosons. "the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as Non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. ...the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the v = 5/2 state."

Anyons are the intermediate state of Life?


Massless fermionic matter (Weyl fermions) and dyons, quasiparticles and quasiholes? Mass determined by the hierarchial energy scales? And hidden gauge fields? How is E=mc^2 true then? It is about a closed Universe. Our Universe is open.

To be continued.

A window into the phenomen of Life?

Hurricanes are characterized by heavy winds spiralling around the eye of the storm. They can be very stable and travel thousands of miles while changing in shape, velocity, rotation speed and strength. Inside the 'wheel' are strong forces born, like infrasounds, magnetic changes and levitation, gravity...

Skyrmions was rediscovered in 1983 in the context of Quantum Chromodynamics (QCD). A skyrmion contains 'knots' in its magnetization; the vector character of the magnetization leads to more complex topological states. The term skyrmion derives from the analogy with the Skyrme model for nucleons in pion (electron, muon, tau) field theory, and is used in the modelling of atomic nuclei as quantized skyrmions. Skyrmions are topological soliton solutions whose conserved topological charge B is identified with the baryon number of a nucleus. Apart from an energy and length scale, the Skyrme model has just one dimensionless parameter m proportional to the pion mass. It has been found that a good fit to experimental nuclear data requires m to be of order 1 (reals?). Modelling of atomic nuclei here.

Roaming through a skyrmion. When an electron moves through a special type of magnetic texture called a skyrmion, its magnetic moment (spin) twists to adjust to the skyrmion's local spin structure (ribbon-like pattern). This twisting changes the electron's direction of travel and pushes the electron and the skyrmion in opposite directions (not shown). From Nature (1).

It is interesting to observe skyrmions in the more conventional, 3-D magnetic system MnSi at higher temperatures. Chlorophyll resembles much MnSi basic unit. Chlorophyll support assembly and accumulation of light-harvesting complexes, only its central atom is Mg and its 'arms' are C. Modifications that introduce electronegative groups on the periphery of the chlorophyll molecule withdraw electrons from the pyrrole nitrogens and thus reduce their basicity. Consequently, the tendency of the central Mg to form coordination bonds with electron pairs in exogenous ligands, a reflection of its Lewis acid properties, is increased, here.


The Dirac world.
There are a force emerging perpendicular to this electron movement, and also consequently a repelling force (antimatter?). This will create a cone of different magnetism (and gravity?) expending forth and back. A non-material Dirac cone creating topology and hierarchy and matter condensation? Gravity emergense in the 4-D? Dirac electrons can only exist on the honeycomb lattice. About the Carbon world:

Graphene's band dispersion and low energy Dirac cone. From EV Castro.

Castros research group:

Graphene is a semi-metal, with a linearly vanishing density of states (DOS) at zero energy (the Fermi level for the undoped material). Near the Fermi energy, the DOS fills up to a constant plateau (also predicted in a CPA) but in addition has a sharp peak closer to zero energy, reminiscent of the delta function of the quasi-localized state for a single impurity. A study of the inverse participation ratio showed that the states contributing to this feature have a real space decay similar to the single impurity state (~1/r, where r is the distance to the vacancy). This work in currently being extended to study long range (Coulomb) impurity potentials.


We also developed a tight-binding study of the graphene bilayer, subject to a perpendicular electric field. This turns out to be a very interesting system for applications, since the bilayer opens a gap, tunable via the external electric field, and managed to obtain a consistent description of the measured cyclotron mass and energy gap as a function of the external field.

We showed that a relative rotation of the layers (a rather common stacking defect in graphite, often observed in STM studies of its surface) has profound effects on the electronic structure near the Fermi level:
* the low energy dispersion remains linear, as in a single layer
* the Fermi velocity can be significantly reduced with respect to the single layer value
* a perpendicular electric field does not open a gap.
Gap opening in a biased graphene bilayer. An energy gap is created if the material is placed between positive and negative electrodes. The gap arises because the transverse voltage causes an excess of negatively charged electrons in one layer and an excess of positively charged “holes” in the other layer. These electrons and holes are believed to pair up to create quasiparticles, which behave differently than their constituent particles.

A magnetic field was also applied to the bilayer, which caused the quasiparticles to move in circular orbits – an effect called cyclotron resonance. The team measured the period of this resonance, which depends on the mass of the quasiparticles. The team discovered that this cyclotron mass increased as the applied voltage increased from zero to about 100 V, allowing them to conclude that the energy gap was also changing from zero to about 150 meV (2).

A peculiar feature of electrons and holes in graphene is that they move through the material as if they have no rest mass – something that makes the material a very good conductor. However, the quasiparticles have a rest mass and according to Castro Neto, this mass leads to an energy gap that must be overcome before current can flow.

What say Castro Neto? He looks at quantum phase transitions and graphene.

Many phases of matter are characterized by order of some electronic degree of freedom such as spin (as in the case of spin density waves - SDW), or charge (as in the case of charge density waves - CDW). Other phases are characterized by more complicated order parameters that are directly related to many-body effects (as in the casea of superconductivity). It is possible to tune between phases with order and without order by tunning some parameter such as the temperature of the system. These finite temperature phase transititons have been well studied in the context of classical critical phenomena. Much less is known by phase transitions that occur at zero temperature in which quantum fluctuations play an important role. These quantum phase transitions (QPT) are responsible for very unusual behavior that cannot be described within traditional theoretical frameworks. QPT transitions can be tuned by the application of pressure, magnetic field, or even chemical modification, that unavoidably introduces disorder in the material. Disorder can strongly affect QPT because quantum fluctuations are very sensitive to geometrical constraints. Cold atom systems, high temperature superconductors, transition metal dichalcogenides, and heavy fermion materials are example of systems where QPT are believed to play an important role.

Example of a Quantum Phase Transition: T is temperature and Fm is a tunning parameter.

Spin and charge densities as opposed to many-body systems, which only them can have superconductions and superpositions. Of course, it takes two to tangos. The Scrödinger cat phenomen...

This is said to be usable for molecular sensors. Surprise? I think at once of sensors in biology. Carbon is central in biology, as also cyclotrone resonances (Liboff, TGD).


Is this 'gap opening' the same as the A-phase? Could this be the quantum window in biology, giving rise to paranormal experiences? And also diseases like MS, arthritis, pain...? The meridian functionings? The beginning of the entangled qubit-thing, used by Rakovic. Some kind of makrostate qubit? A chrystalline living oscillating phase that can be managed by small changes in temp.,pressure, pH? This list sound familiar from the nerve pulse. But how learn to dance?.


Chrystals of different kinds. The A-phase.
The abstract to another Nature article 17.6 (3).

Crystal order is not restricted to the periodic atomic array, but can also be found in electronic systems such as the Wigner crystal or in the form of orbital order, stripe order and magnetic order. In the case of magnetic order, spins align parallel to each other in ferromagnets and antiparallel in antiferromagnets (= diamagnetic and paramagnetic order?) In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures. Among them is the unusual, topologically stable skyrmion spin texture, in which the spins point in all the directions wrapping a sphere, the skyrmion. The skyrmion configuration in a magnetic solid is anticipated to produce unconventional spin–electronic phenomena such as the topological Hall effect. The crystallization of skyrmions as driven by thermal fluctuations has recently been confirmed in a narrow region of the temperature/magnetic field (T–B) phase diagram in neutron scattering studies of the three-dimensional helical magnets MnSi and Fe1−xCoxSi. With a magnetic field of 50–70 mT applied normal to the film, we observe skyrmions in the form of a hexagonal arrangement of swirling spin textures, with a lattice spacing of 90 nm. The related T–B phase diagram is found to be in good agreement with Monte Carlo simulations. In this two-dimensional case, the skyrmion crystal seems very stable and appears over a wide range of the phase diagram, including near zero temperature. Such a controlled nanometre-scale spin topology in a thin film may be useful in observing unconventional magneto-transport effects.

a, b, Helical (a) and skyrmion (b) structures predicted by Monte Carlo simulation. c, Schematic of the spin configuration in a skyrmion. d–f, The experimentally observed real-space images of the spin texture, represented by the lateral magnetization distribution as obtained by TIE analysis of the Lorentz TEM data: helical structure at zero magnetic field (d), the skyrmion crystal (SkX) structure for a weak magnetic field (50 mT) applied normal to the thin plate (e) and a magnified view of e (f). The colour map and white arrows represent the magnetization direction at each point.

a–c, Spin textures observed using Lorentz TEM obtained by Monte Carlo simulation. e–g, Spin textures after TEM. H, helical structure; SkX, skyrmion crystal structure; FM, ferromagnetic structure. d, h, Observed (d) and calculated (h) phase diagrams in the B–T plane. The colour bars in the phase diagrams indicate the skyrmion density per 10−12 m2 (d) and per d2 (h), d being the helical spin wavelength. Dashed lines show the phase boundaries between the SkX, H and FM phases. Stars in d and h indicate (T, B) conditions for the images shown in a–c and e–g, respectively.

Molecular orbital theory (4):
A molecular orbital is the volume within which a high percentage of the negative charge generated by the electron is found. The molecular orbital volume encompasses the whole molecule. The electrons would fill the molecular orbitals of molecules like electrons fill atomic orbitals in atoms.
- The molecular orbitals are filled in a way that yields the lowest potential energy for the molecule.
- The maximum number of electrons in each molecular orbital is two (Pauli exclusion principle.)
- Orbitals of equal energy are half filled with parallel spin before they begin to pair up (Hund's Rule.)
- Molecular orbitals are formed from the overlap (superpositions?) of atomic orbitals.
- Only atomic orbitals of about the same energy interact to a significant degree.
- When two atomic orbitals overlap, they interact in two extreme ways to form two molecular orbitals, a bonding molecular orbital and an antibonding molecular orbital.

Light waves can interact in-phase, which leads to an increase in the intensity of the light (brighter) and out-of-phase, which leads to a decrease in the intensity of the light (less bright). Electron waves can also interact in-phase and out-of-phase. In-phase interaction leads to an increase in the intensity of the negative charge. Out-of-phase interaction leads to a decrease in the intensity of the negative charge.

In-phase leads to wave enhancement similar to the enhancement of two in-phase light waves. Where the atomic orbitals overlap, the in-phase interaction leads to an increase in the intensity of the negative charge in the region where they overlap. This creates an increase in negative charge between the nuclei and an increase in the plus-minus attraction between the electron charge and the nuclei for the atoms in the bond. The greater attraction leads to lower potential energy.
Because electrons in the molecular orbital are lower potential energy than in separate atomic orbitals, energy would be required to shift the electrons back into the 1s orbitals of separate atoms. This keeps the atoms together in the molecule, so we call this orbital a bonding molecular orbital. The molecular orbital formed is symmetrical about the axis of the bond. Symmetrical molecular orbitals are called sigma, σ, molecular orbitals.

The second way that two atomic orbitals interact is out-of-phase. Where the atomic orbitals overlap, the out-of-phase interaction leads to a decrease in the intensity of the negative charge. This creates a decrease in negative charge between the nuclei and a decrease in the plus-minus attraction between the electron charge and the nuclei for the atoms in the bond. The lesser attraction leads to higher potential energy. The electrons are more stable in the 1s atomic orbitals of separate atoms, so electrons in this type of molecular orbital destabilize the bond between atoms. We call molecular orbitals of this type antibonding molecular orbitals. The molecular orbital formed is symmetrical about the axis of the bond, so it is a sigma molecular orbital with a symbol of σ*1s.
This is an simple box, like a Feynman diagram.
When two larger atoms atoms combine to form a diatomic molecule (like O2, F2, or Ne2), more atomic orbitals interact. The LCAO approximation assumes that only the atomic orbitals of about the same energy interact. For O2, F2, or Ne2, the orbital energies are different enough so only orbitals of the same energy interact to a significant degree.

The two 2py atomic orbitals overlap in parallel and form two pi molecular orbitals. Pi molecular orbitals are asymmetrical about the axis of the bond.

bond order = 1/2 (#e- in bonding MO's - #e- in antibonding MO's)

Oxygen, the negentropic element.
The molecular orbital diagram for a diatomic oxygen molecule, O2.


- O2 has a bond order of 2. Bond Order = 1/2(10 - 6) = 2
- The bond order of two suggests that the oxygen molecule is stable.
- The two unpaired electrons show that O2 is paramagnetic.
The bond between the carbon and oxygen in carbon monoxide is very strong despite what looks like a strange and perhaps unstable Lewis Structure. The plus formal charge on the more electronegative oxygen and the minus formal charge on the less electronegative carbon would suggest instability. The molecular orbital diagram predicts CO to be very stable with a bond order of three. About the geometry of molecular orbits here.

Other odd features.
Coexistence of both magnetic order and cooperative paramagnetic spin liquid behavior is possible, seen in spin glass phenomens, as instance. The temperature Tc is joined to a point in the phase diagram where a transition between two paramagnetic solutions happens. This gives liquid crystal properties, called a mesophase? "The existence of a long range intermolecular exchange interaction at all the temperatures is established by the collapse of the hyperfine structure in the spectra of the condensed samples. The comparison of the principal effective g- values in the solid phase with those of the isolated molecule obtained from the toluene solution spectra indicates that in the solid, the molecules pack keeping their molecular axes parallel. The drastic changes observed in the spectra when the sample reaches the smectic phase are interpreted as a consequence of the structure of this mesophase".
Long-range polarization in an antiferrimagnetic order has also shown a window of ferromagnetic order. An emergence of 2-D? An temp. dependent interference between the electric and magnetic properties? It is shown that there exists a transition between a Néel state and a quantum paramagnetic phase, characterized by broken translational invariance. The non-magnetic phase preserves the lattice rotational symmetry, and has a correlated plaquette nature.
A mirror symmetry is identified to characterize both electron and impurity magnetizations (spin polarizations) when the impurities are symmetrically (with respect to this mirror) positioned and when pinning fields are absent.

Fluorescence polarization and electron paramagnetic resonanse spectroscopy are used to study order and orientation of protein elements in biology.


Life is these multiphases? As Rakovic said, Life is not trying to eliminate the noise, but to use it to create oscillations and a new order. That is exactly some kind of superpositions of different em-properties (liquid chrystals?).

Organization.
In oxides the O is shown to be important for the topology. It brings in the 'islands'. Here.
...homolog but also that grain boundaries are the preferential sites for oxide nucleation and the oxide islands formed along the grain boundaries show a faster growth rate than that on flat Cu surface. The oxidation on the faceted Cu(110) surface results in heterogeneous nucleation of oxide islands in the facet valleys and one-dimensional growth along the intersection direction of the facets. Self-organised nanostructures, obtained by oxidation of III–VI compounds It was established that self oxide surfaces possess numerous geometrical morphologies of nanostructures (wires, trees, self assembled networks).

The spin states are analogs to solitons? The charged excitations are very light, and form a degenerate Bose gas even at high temperatures. -> Oxide superconductors.
Ahn:

Complex oxide materials exhibit a tremendous diversity of behavior encompassing a broad range of functional properties, such as magnetism, ferroelectricity, and superconductivity. As diverse as this behavior is, an even richer spectrum of possibilities becomes available if one starts to combine different complex oxides together with atomic-scale precision to create new artificially structured, heterogeneous systems.

Quantum spin Hall effect in a transition metal oxide Na2IrO3 an antiferromagnetic order first develops at the edge, and later inside the bulk at low temperatures. The nontrivial topology is more ubiquitous in solids than expected.

A recent breakthrough in this field is the theoretical and experimental discoveries of the quantum spin Hall (QSH) effect in time-reversal symmetric insulators. Intuitively it can be regarded as two copies of QH systems with up and down spins, but is driven by the spin-orbit interaction (SOI) instead of the external magnetic field. The topological insulator is closely related to a Kramers doublet protected by the time-reversal symmetry, and corresponds to the presence or absence of gapless helical edge modes in the semi-infinite system.

The theoretical design of a topological insulator using HgTe/CdTe quantum wells, and it is shown that the lowtemp superconduction relies on large SOI and the fine tuning of the band structure. Therefore one important development is to realize more robust topological insulators at higher temperature by the larger SOI. Try to design topological insulators in 5d transition metal oxides by using the complex transfer integrals and the lattice geometry, which was shown.

Another interesting development is to study the interplay between the non-trivial topology and the electron correlation. Generally the electron correlation is stronger in d- and f-electrons than in s- and p-electrons. When we look at transition metal ions in the periodic table, the electron correlation is the strongest in 3d elements and decreases to 4d and to 5d elements because d-orbitals are more and more extended, while the SOI increases as the atomic number.

5d-orbitals are rather extended and subject to the large crystalline field. Under the octahedral crystalline field, d-orbitals are split into e(g) (x2 − y2, 3z2 − r2)- and t(2g) (xy, yz, zx)-orbitals by 10Dq of the order of 3eV. The SOI is quenched in e(g)-orbitals but remains effective in t(2g)-orbitals, which form effectively the triplet with ℓ(eff) = 1. Including the SOI, we obtain the states with the total angular momentum j(eff) = 3/2 and 1/2. The central idea is that the transfer integrals between these complex orbitals and oxygen orbitals become complex. This complex transfer integral is responsible for topological states in iridates ( - look also at the molecular orbital model).


Na2IrO3 whose layered crystal structure contains the honeycomb lattice, with each Ir atom surrounded by an octahedron of six O atoms, which leads to the similar energy level scheme as Sr2IrO4, i.e. one electron in j(eff) = 1/2-states, we can construct the effective single-band model on the honeycomb lattice. Since the O p-level ǫp are around 3eV lower than the Ir d-level ǫd we can integrate out p-orbitals to obtain the following effective Hamiltonian where [ij] and [[ij]] denote the nearest-neighbor (NN) and next-nearest-neighbor (NNN) pairs, respectively. The transfer integral t between a NN pair is real and spin-independent. The transfer integral between a NNN pair depends on spin, leading to a topological insulator, perpendicular to the honeycomb plane. With this convention, the transfer integral is a 2 × 2 matrix in the spin space. The key to these complex transfer integrals is the asymmetry between two paths connecting a NNN pair. The real transfer integral t′0 can be produced by the direct dd hopping and breaks the particle-hole symmetry.

To summarize these results, the transfer integrals are real and spin-independent for a NN pair, while complex and spin-dependent for a NNN pair, where ψ(~r) is the eight-component spinor field operator, and kX and kY are measured from K or K′ points. η’s, τ’s, and σ’s are the Pauli matrices for the valley (K or K′), sublattice (1 or 2), and spin (+ or −) degrees of freedom, respectively. Diagonally is a zig-zag geometry. The crossing point is at k = π for the zig-zag geometry, while at k = 0 for the armchair geometry, where k is the wavenumber along the edge. Anyway such crossing is protected by the Kramers theorem, and can get gapped only if the time-reversal symmetry is broken.

Chirality.
The circular movement in the skyrmions give rise to an helix. Carbon is an asymmetric molecule giving chirality.

Carbon is also one possible way Dirac electrons will enter. And Carbon will form a superposition upon the hexameric lattice as a trimeric sublattice. Oxygenal secondary lattice is hexagonal. I think this is very important in biology.


The intensity pattern in the A-phase is characterized by a six-fold symmetry. These patterns are exclusively seen in the plane perpendicular to the magnetic field. The A-Phase can be identfii ed as a hexagonal lattice of skyrmion tubes. The spin structure in the A-phase of MnSi is a so-called triple-Q state, i.e., a superposition of three helices under 120 degrees, and similar to the vortex lattice in superconductors.

Twenty years ago it has been predicted that skyrmions exist in anisotropic spin systems with chiral spin-orbit interactions, where they are expected to form crystalline structures. The origin of the topological Hall effect is a Berry phase collected by the conduction electrons when following adiabatically the spin polarization of topologically stable knots in the spin structure. Thus the Berry phase reflects the chirality and winding number of the knots. The topological Hall effect arises besides the normal Hall effect, which is proportional to the applied magnetic field, and the anomalous Hall effect that scales with ferromagnetic components of the magnetization.

This provides clear experimental evidence that the magnetic structure observed in neutron scattering has indeed the topological properties (chirality and winding number). The helimagnetic state may be understood as the result of a hierarchy of energy scales where ferromagnetic exchange is on the strongest scale and the isotropic spin-orbit interactions due to the lack of inversion symmetry give rise to a long-wavelength helimagnetic modulation, where wavelength of h is about 190Å. The propagation vector ~Q of the helix is pinned to the cubic spacediagonal by higher order spin-orbit coupling terms, which represent the weakest scale.

1. Ordered states with helical arrangement of the magnetic moments are described by a chiral order parameter which yields the left- or right-handed rotation of neighboring spins along the pitch of the helix.

2. Spins on a frustrated lattice form another class of systems, where simultaneous ordering of chiral and spin parameters can be found. Ex. triangular lattice with antiferromagnetic nearest neighbor interaction, the classical ground-state is given by a non-collinear arrangement with the spin vectors forming a 120◦ structure. In this case, the ground state is highly degenerate as a continuous rotation of the spins in the hexagonal plane leaves the energy of the system unchanged. In addition, it is possible to obtain two equivalent ground states which differ only by the sense of rotation (left or right) of the magnetic moments from sublattice to sub-lattice, hence yielding an example of chiral degeneracy.

3. CP breaking is the basic prediction of TGD and relates to the CP breaking of Chern-Simons action inducing CP breaking in the modified Dirac action defining the fermionic propagator. Chiral selection requires parity breaking, and the parity breaking of the molecule itself would induce the symmetry breaking if molecule possesses dark magnetic body., says Matti Pitkänen. I take my freedom to translate this magnetic body to the Dirac cone, (and it can also be seen as a wormhole?). DM-interaction depends on the polarization with respect to the magnetic vectors. The required asymmetry is a consequence of the cone, with one part dark, 'taking away' about half of the interacting particles, so that the effeciency of the reaction pathways can be much higher.

Water can be an interacting, reducing medium in this process. Conformal changes in proteins are also important as environmental influences. As are oxygen, of course, and other biomolecules.

4. Chiral fluctuations can be directly observed in non-centrosymmetric crystals without disturbing the sample by a magnetic field. polarized inelastic neutron scattering experiments performed in the paramagnetic phase of the itinerant ferromagnet MnSi that confirm the chiral character due to spin-orbit coupling. Antisymmetric (in forming the magnetic groundstate) and asymmetric interactions are possible.

Time can also be seen as a chiral structure?

5. There are a possibility for more than one mirror image, an hierarchy of particles can be created, but usually the other mirrorimages are dark (too low energy). TGD talks of an fractional quantum Hall effect.


Life as Islands.
Life is 'emergent'. It use the same atoms and molecules as rest of the matter, but maybe in one aspect Life is different. Life is built on hexagons. Life interact with the quantum world in many ways. It is important to keep that interaction at moderate levels, said Rakovic and Pitkänen, for organizational reasons.

One of the most fascinating aspects of physics is the 'emergence' of complex structures out of simple laws, an interesting case of which are structures protected by topological invariants. To illustrate an example of this, consider vortex lines in superconductors. In such systems, the phase of the Cooper-pair wave function rotates by 2πn as one circles a vortex. Continuity then requires the vorticity n to be an integer. For this reason, a vortex with n=±1 cannot decay.

Stabile topological structures lies behind biology. The stability are rationals, the oscillations are p-adics? The glue are entanglement in electon-sheets? Dirac-electrons are p-adics? One important task is to clearly define this interaction of stabilizating chaos. Life is complex.

TGD: The recent claim could be explained if antineutrinos and neutrinos in the experimental situation favor different p-adic primes p≈ 2k. If one has k(ν)=k(νbar)+1 for all families and the topological mixing matrices are otherwise the same (recall that fermion families correspond in the absence of mixing to different topologies for wormhole throats: sphere, torus, sphere with two handles, perhaps also higher families although there is good argument supporting the view that three lowest genera are "light").

Another kind of fraction is the cyclotrone resonance giving rise to molecular sensing?

The third one is the topological changes with distance and time? Then also the cognition, memory and the consciousness follows as a natural aspect.

Matti Pitkänen writes: A good guess is that algebraic entanglement is essential for quantum computation, which therefore might correspond to a conscious process. Hence cognition could be seen as a quantum computation like process, a more approriate term being quantum problem solving. Living-dead dichotomy could correspond to rational-irrational or to algebraic-transcendental dichotomy: this at least when life is interpreted as intelligent life. Life would in a well defined sense correspond to islands of rationality/algebraicity in the seas of real and p-adic continua.

Algebraic numbers are related to rationals by a finite number of algebraic operations (Gaussian distribution?) and are intermediate between periodic and chaotic orbits* allowing an interpretation as an element in an algebraic extension of any p-adic number field. The projections of the orbit to various coordinate directions of the algebraic extension represent now periodic orbits.

*) Chaotic orbits should be interpreted as potential possibilities?

The special nature of the Golden Mean, which involves 5^1/2, conforms the view that algebraic numbers rather than only rationals are essential for life. And may I fill in, spheres? One especially interesting aspect with this skyrmionic atomic model is that the Platonic solids are found directly from it.

The new secondary p-adic time scales assigned with elementary particles, in particular the .1 second time scale assignable with electron as time scale of corresponding "causal diamond" and defining fundamental biorhythm will mean a direct connection between living and dead matter. Time and entropy are so important for life to give the coherence. The chrystal phases is entanglement, or SOL-phases in biology.

Water, temp., pressure, pH etc. increases the 'noise' and hence the reactivity. Together with inhibition noise gives coherence in the different systems, so they can behave as entangled quantum dots, at least for a while. As instance when the chromophore is in excited state as opposite electronic ground state.

The basic prediction of zero energy ontology is that second law does not make sense in the time scale below the time scale defined by the temporal size of CD for physics associated with the field body of system in question - say electron, say Matti.

Complex structures are function of entropic/negentropic forces as amplified forces drive spatial expansion of matter. If this oscillation is a vortex the apex is also spiralling up. Stability = rationals, oscillation = complex numbers?

The gap opening is the window into the quantum world?


References.
1. Condensed-matter physics: Single skyrmions spotted
Christian Pfleiderer & Achim Rosch: Nature Volume: 465,
Pages: 880–881 (17 June 2010) DOI: doi:10.1038/465880a

2. News. Dec 5, 2007 Tuneable gap semiconductor is a first Gapless semiconductor. http://physicsworld.com/cws/article/news/32085;jsessionid=34FB29F720E6613E9DC...

http://www.thp.uni-koeln.de/rosch/publikationen.htm
http://www.worldscibooks.com/physics/7397.html modelling of atomic nuclei.
http://www.springerlink.com/content/u6wl394757m80518/fulltext.pdf chlorophyll
http://faraday.fc.up.pt/cfp/Members/evcastro
http://physics.bu.edu/~neto/ quantum phase transition, theorists are being forced to revisit the conceptual basis for the theory of metals. http://arxiv.org/ftp/arxiv/papers/1003/1003.4520.pdf

3. Real-space observation of a two-dimensional skyrmion crystal
X. Z. Yu, Y. Onose, N. Kanazawa, J. H. Park, J. H. Han, Y. Matsui, N. Nagaosa & Y. Tokura
Nature 465, 901-904 (17 June 2010) | doi:10.1038/nature09124
http://www.nature.com/nature/journal/v465/n7300/full/nature09124.html

4. MO-theory. Mark Bishop, http://www.mpcfaculty.net/mark_bishop/molecular_orbital_theory.htm http://arxiv.org/ftp/arxiv/papers/1001/1001.2021.pdf

http://arxiv.org/PS_cache/arxiv/pdf/0902/0902.1933v2.pdf
http://arxiv.org/PS_cache/cond-mat/pdf/0201/0201327v1.pdf

http://tgdtheory.com/public_html/articles/spinstructure.pdf
http://tgdtheory.com/public_html/hologram/nhologram2009.html#chiralselection