Probabilities and Path-Integral Realization of Exclusion Statistics

TL;DR

This paper presents a microscopic formulation of exclusion statistics using occupation probabilities, introduces a path-integral realization applicable to interacting systems, and proves the zero-temperature heat capacity vanishing for such systems.

Contribution

It provides a novel microscopic framework for exclusion statistics and a generalizable path-integral approach for interacting systems.

Findings

Negative probabilities are necessary for fractional statistics.

A path-integral realization for exclusion statistics is derived.

Heat capacity vanishes at zero temperature for exclusion statistics systems.

Abstract

A microscopic formulation of Haldane's exclusions statistics is given in terms of a priori occupation probabilities of states. It is shown that negative probabilities are always necessary to reproduce fractional statistics. Based on this formulation, a path-integral realization for systems with exclusion statistics is derived. This has the advantage of being generalizable to interacting systems, and can be used as the starting point for further generalizations of statistics. As a byproduct, the vanishing of the heat capacity at zero temperature for exclusion statistics systems is proved.