### How the effective hierarchy of Planck constants could reveal itself in condensed matter physics?

Phil Anderson - one of the gurus of condensed matter physics - has stated that there exists no theory of condensed matter: experiments produce repeatedly surprises and theoreticians do their best to explain them in the framework of existing quantum theory.

This suggests that condensed matter physics might allow room even for new physics. Indeed, the model for fractional quantum Hall effect (FQHE) strengthened the feeling that the many-sheeted physics of TGD could play a key role in condensed matter physics often thought to be a closed chapter in physics. One implication would be that space-time regions with Euclidian signature of the induced metric would represent the space-time sheet assignable to condensed matter object as a whole as analog of a line of a generalized Feynman diagram. Also the hierarchy of effective Planck constants hbar_{eff} =n×hbar appears in the model of FQHE.

The recent TGD inspired discussion of possibility of quantum description of psychokinesis boils down to a model for intentional action based on the notion of magnetic flux tube carrying dark matter and dark photons and inducing macroscopic quantum superpositions of magnetic bubbles of ferromagnet with opposite magnetization. As a by-product the model leads to the proposal that the conduction electrons responsible for ferromagnetism are actually dark (in the sense of having large value of effective Planck constant) and assignable to a multi-sheeted singular covering of space-time sheet assignable to second quantization multifurcation of the preferred extremal of Kähler action made possible by its huge vacuum degeneracy.

What might be the signatures for hbar_{eff}=n×hbar states in condensed matter physics and could one interpret some exotic phenomena of condensed matter physics in terms of these states for electrons?

- The basic signature for the many-electron states associated with multi-sheeted covering is a sharp peak in the density of states due to the presence of new degrees of freedom. In ferromagnets this kind of sharp peak is indeed observed at Fermi energy.

- In the theory of super-conductivity Cooper pairs are identified as bosons. In TGD framework all bosons - also photons - emerge as wormhole contacts with throats carrying fermion and antifermion. I have always felt uneasy with the assumption that two-fermion states obey exact Bose-Einstein statistics at the level of oscillator operators: they are after all two-fermion states. The sheets of multi-sheeted covering resulting in a multifurcation could however carry both photons identified as fermion-antifermion pairs and Cooper pairs and this could naturally give rise to Bose-Einstein statistics in strong sense and also be involved with Bose-Einstein condensates. The maximum number of photons/Cooper pairs in the Bose-Einstein condensate would be given by the number of sheets. Note that in zero energy ontology also the counterparts of coherent states of Cooper pairs are possible: in positive energy ontology they have ill-defined fermion number and also this has made me feel uneasy.

- Majorana fermions have become one of the hot topics of condensed matter physics recently.

- Majorana particles are actually quasiparticles which can be said to be half-electrons and half-holes. In the language of anyons would would have charge fractionization e→ e/2. The oscillator operator a
^{†}(E) creating the hole with energy E defined as the difference of real energy and Fermi energy equals to the annihilation operator a(-E) creating a hole: a^{†}(E)=a(-E). If the energy of excitation is E=0 one obtains a^{†}(0)=a(-0).

Since oscillator operators generate a Clifford algebra just like gamma matrices do, one can argue that one has Majorana fermions at the level of Fock space rather than at the level of spinors. Note that one cannot define Fock vacuum as a state annihilated by a(0). Since the creation of particle generates a hole equal to particle for E=0, Majorana particles come always in pairs. A fusion of two Majorana particles produces an ordinary fermion.

- Purely mathematically Majorana fermion as a quasiparticle would be highly analogous to covariantly constant right-handed neutrino spinor in TGD with vanishing four-momentum. Note that right-handed neutrino allows 4-dimensional modes as a solution of the modified Dirac equation whereas other spinor modes localized to partonic 2-surfaces and string world sheets. The recent view is however that covariantly constant right-handed neutrino cannot not give rise to the TGD counterpart of standard space-time SUSY.

- In TGD framework the description that suggests itself is in terms of bifurcation of space-time sheet. Charge -e/2 states would be electrons delocalized to two sheets. Charge fractionization would occur in the sense that both sheets would carry charge -e/2. Bifurcation could also carry two electrons giving charge -e at both sheets. Two-sheeted analog of Cooper pair would be in question. Ordinary Cooper pair would in turn be localized in single sheet of a multifurcation. The two-sheeted analog of Cooper pair could be regarded as a pair of Majorana particles if the measured charge of electron corresponds to its charge at single sheet of bifurcation (this assumption made also in the case of FQHE is crucial!). Whether this is the case, remains unclear to me.

- Fractional Josephson effect in which the current carriers of Josephson current become electrons or quasiparticles with the quantum numbers of electron has been suggested to serve as a signature of Majorana quasiparticles. An explanation consistent with above assumption is as a two-sheeted analog of Cooper pair associated with a bifurcated space-time sheets.

If the measurements of Josephson current measure the current associated with single branch of bifurcation the unit of Josephson current is indeed halved from -2e to -e. These 2-sheeted Cooper pairs behave like dark matter with respect to ordinary matter so that dissipation free current flow would become possible.

Note that ordinary Cooper pair Bose-Einstein condensate would correspond to N-furcation with N identified as the number of Cooper pairs in the condensate if the above speculation is correct. Fractional Josephson effect generated in external field would correspond to a formation of mini Bose-Einstein condensates in this framework and also smaller fractional charges are expected. In this case the interpretation as Majorana fermion does not seem to make sense.

- Majorana particles are actually quasiparticles which can be said to be half-electrons and half-holes. In the language of anyons would would have charge fractionization e→ e/2. The oscillator operator a

For more details see the chapter Does TGD Predict Spectrum of Planck Constants? of "Towards M-Matrix".

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