Path Integrals and Parastatistics

TL;DR

This paper derives path integrals for particles obeying parastatistics, revealing how topological sectors relate to permutation parity, and proposes generalized statistics maintaining unitarity and cluster decomposition.

Contribution

It introduces a derivation of propagators and path integrals for parastatistics and proposes generalized statistics consistent with key physical principles.

Findings

Statistical weights relate to permutation parity.

Generalized statistics obey unitarity and cluster decomposition.

Maximal occupancy statistics require ghost states.

Abstract

The propagator and corresponding path integral for a system of identical particles obeying parastatistics are derived. It is found that the statistical weights of topological sectors of the path integral for parafermions and parabosons are simply related through multiplication by the parity of the permutation of the final positions of the particles. Appropriate generalizations of statistics are proposed obeying unitarity and factorizability (strong cluster decomposition). The realization of simple maximal occupancy (Gentile) statistics is shown to require ghost states.