Non-Invariant Ground States, Thermal Average, and generalized Fermionic Statistics

TL;DR

This paper introduces a framework linking non-invariant ground states to generalized fermionic statistics, exploring thermal averages, supersymmetric constructions, and phase transition implications for quantum systems.

Contribution

It proposes a novel approach connecting ground state invariance to generalized fermionic statistics and introduces a supersymmetric statistical framework.

Findings

Occupation number depends on ground state mixing

Supersymmetric statistics construction provided

Vacuum structure linked to phase transition

Abstract

We present an approach to generalised fermionic statistics which relates the existence of a generalised statistical behaviour to non-invariant ground states. Considering the thermal average of an operatorial generalization of the Heisenberg algebra, we get an occupation number which depends on the degree of mixing between symmetric and antisymmetric sectors of the ground state. A natural prescription is given for the construction of a supersymmetric statistics. We also show that the structure of the vacuum, and therefore the statistical behaviour of the system, can be accounted for in terms of a second order phase transition.