Permutation Invariant Statistics, Duality and Simple Interpolations

TL;DR

This paper explores permutation invariant statistics in quantum systems, introduces simple interpolations between different types of particles, and extends these concepts to anyonic-like statistics, revealing new connections and minimal interpolations.

Contribution

It introduces a new minimal interpolation between parabosons and parafermions of any order, and extends the framework to anyonic-like statistics.

Findings

Constructed simple interpolations between dual statistics.

Established connection between boson-fermion mixing and dual statistics.

Extended the construction to anyonic-like statistics.

Abstract

General permutation invariant statistics in the second quantized approach are considered. Simple interpolations between dual statistics are constructed. Particularly, we present a new minimal interpolation between parabosons and parafermions of any order. The connection with a simple mixing between bosons and fermions is established. The construction is extended to anyonic-like statistics.