Flux tube condensates as a basic deviation between TGD from QFT descriptions and phases, which are not Fermi liquids

The large value of h_eff has besides number theoretical interpretation (see this) also a geometric interpretation. Space-time surface can be regarded as many-sheeted over both M⁴ and CP₂. In the first case the CP₂ coordinates are many-valued functions of M⁴ coordinates. In the latter case M⁴ coordinates are many-valued functions of CP₂ coordinates so that QFT type description fails. This case is highly interesting in the case of quantum biology. Since a connected space-time surface defines the quantum coherence region, an ensemble of, say, monopole flux tubes can define a quantum coherent region in the latter case: one simply has an analog of Bose-Einstein condensate of monopole flux tubes.

The flux tube condensate as a covering of CP₂ means a dramatic deviation from the QFT picture and is a central notion in the applications of quantum TGD to biology. Therefore some examples are in order.

1. Fermi liquid description of electrons relies on the notion of a quasiparticle as an electron plus excitations of various kinds created by its propagation in the lattice. In some systems this description fails and these systems would. have a natural description in terms of space-time surfaces which are multiple coverings of CP₂, say flux tube condensates.
2. In high Tc superconductors and bio-superconductors (see this and this) the space-time surface could correspond to this kind of flux tube condensates and Cooper pairs would be fermion pairs with members at separate flux tubes. The connectedness of the space-time surface having about h_eff/h=n flux tubes would correlate the fermions.
3. Bogoliubov quasiparticles related to superconductors are regarded as superpositions of electron excitation and hole. The problem is that they have an ill-defined fermion number. In TGD, they would correspond to superpositions of a dark electron accompanied by a hole which it has left behind and therefore having a well-defined fermion number. Bogoliubov quasiparticle is indeed what can be seen using the existing experimental tools and physical understanding.
4. Strange metals would be an example of a system having no description using quasiparticles, as the linear dependence of the resistance at low temperatures demonstrates. I have considered a description of them in terms of Cooper pairs at short closed flux tubes (see this and this: this would however suggest a vanishing resistance in an ideal situation. Something seems to go wrong.

   An alternative description could be in terms of superpositions of dark electrons and holes assignable to the flux tube condensate. Strange metal is between Fermi liquid and superconductor: this conforms with the fact that strange metals are quantum critical systems. The transition to high Tc superconductivity is preceded by a transition to a phase in which something resembling Cooper pairs is present.

   A natural looking interpretation would be in terms of a flux tube condensate and pairs of dark and ordinary electrons. Also now the flux tubes could be short. In the article Comparing the Berry phase model of super-conductivity with the TGD based model), I have considered the possibility that high Tc superconductors could be this kind of "half-superconductors" but this option seems to be wrong.

   The phase transitions between "half-superconductivity" and superconductivity could play a central role also in living matter.

See the article New findings related to the chiral selection or the chapter Quantum Mind, Magnetic Body, and Biological Body.

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.