Derivation of Bose-Einstein and Fermi-Dirac statistics from quantum mechanics: gauge-theoretical structure

TL;DR

This paper derives Bose-Einstein and Fermi-Dirac statistics from quantum mechanics using gauge-theoretical structures, linking statistical ensembles to quantum interactions and symmetry principles.

Contribution

It introduces a gauge-theoretical framework to derive statistical mechanics from quantum principles, unifying the treatment of bosons and fermions.

Findings

Interaction Hamiltonians generate entanglement patterns for ensembles.

Gauge symmetry underpins the statistical distributions.

Relation between random phases and decoherence is discussed.

Abstract

A possible quantum-mechanical origin of statistical mechanics is discussed, and microcanonical and canonical ensembles of bosons and fermions are derived from the stationary Schr\"odinger equation in a unified manner. The interaction Hamiltonians are constructed by the use of the discrete phase operators and the gauge-theoretical structure associated with them. It is shown how the interaction Hamiltonians stipulated by the gauge symmetry generate the specific patterns of entanglement that are desired for establishing microcanonical ensembles. A discussion is also made about the interrelation between random phases and perfect decoherence in the vanishing-interaction limit.