- The integer n corresponds to a dimension of extension of rationals associated with a polynomial determining space-time surface as surface in M8 mapped to H=M4×CP2 by M8-H duality. n corresponds also to the order of the Galois group acting as a symmetry group.
- Galois confinement suggests a universal mechanism for bound state formation: physical states are composites of particles with momenta coming as are algebraic integers. The components of total 4-momentum would be ordinary integers by periodic boundary conditions. This mechanism has also generalization: one has Galois singlet wave function in the space of momenta with components as algebraic integers.
- As a rule, particle energies increase with heff and the analog of "metabolic energy feed" is needed to prevent the reduction of heff to h. In living matter the function of metabolism is just this.
- The phase transitions increasing heff are possible in the presence of energy feed. Bose-Einstein condensation and formation of Cooper pairs (and even states with a larger number of particles, such as 4 electrons as observed recently) could be examples of this. The binding energy of the composite would compensate for the energy needed to increase heff. Fermi statistics with algebraic integer valued momenta allows more Galois confined bound states with a given energy favoring therefore the occurrence of the phase transition.
- Phase transitions quite generally have the property that a small seed induces the phase transition. This would predict that the presence of dark matter favors the emergence of more dark matter.
For a summary of earlier postings see Latest progress in TGD.
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