Fermion scattering as conformal dissipation

The quantal view fermionic of the time evolution as analog of Brownian motion can be made more detailed and this makes it clear that something very different from the quantum field theoretic description of scattering is in question. The interpretation as analog of dissipative time evolution is suggestive. The dissipation could be related to the scaling generator h of conformal algebra, which defines an additive conformal quantum number and is proportional to the mass squared operator m². Dissipation indeed gives rise to the arrow of time making sense both at the level of both space-time and momentum space.

1. At the single particle level, energy dissipation corresponds to a gradual reduction of energy and approach to thermal equilibrium. Analogously, the dissipation for the conformal weight identified as mass squared dissipation would lead from high mass states as unstable on-mass-shell states via unstable virtual states to low mass on-mass-shell states stable in the time scale considered. Asymptotically the evolution would preserve mass squared in M⁸ and the corresponding value of a in M⁴⊂ H. This conformal analog of elastic scattering would preserve mass squared and the conformal dissipation would transform to energy dissipation for stable particles.
2. M⁸-H duality is an inversion M⁴⊂ H → M⁴⊂ M⁸ so that the time evolution as the increase of the values of the light-cone proper time a for CD would correspond to decrease of the mass scales. The largest values of a in time evolution would correspond to the smallest values of mass m² in dissipative evolution for h and at the last steps the masses for stable particles would not change anymore.
3. p-Adic cooling proposed to be behind the production of solar wind and solar energy would be a basic example of this kind of dissipation. M₈₉ hadron physics would be realized at the magnetic monopole flux tubes at the surface layers of the Sun (see this). p-Adic cooling would be a cascade leading from M₈₉ hadron physics to the ordinary M₁₀₇ hadron physics via virtual hadron physics labelled by p-adic primes p≈ 2^k near power 2 with k in the range [89,107].
4. This means a unification of quantum theory and thermodynamics. Zero energy ontology, replacing 3-surfaces with their slightly non-deterministic time evolutions, implies that thermodynamic description and kinetic equations need not be added as additional elements to the quantum description provided by the scattering amplitudes.
5. The following detail is worth noticing. In fermion pair creation, the two-valuedness of the map H→ M⁸ means that the members of the fermion pair have identical masses. Also the Brownian scattering conserves the value of mass squared but not energy.

See the article About the construction of the scattering amplitudes using M⁸-H duality or the chapter with the same title.

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.