Identical Particles and Quantum Symmetries

TL;DR

This paper addresses how Bose-Fermi statistics can be compatible with quantum symmetries using a twisted realization of symmetric groups via unitary transformations.

Contribution

It introduces a method to reconcile particle statistics with quantum symmetries through a novel conjugation approach involving compact quantum groups.

Findings

Achieves compatibility of Bose-Fermi statistics with quantum symmetries

Develops a twisted realization of symmetric groups S_n

Provides a framework for symmetry transformations in quantum particle systems

Abstract

We propose a solution to the problem of compatibility of Bose-Fermi statistics with symmetry transformations implemented by compact quantum groups of Drinfel'd type. We use unitary transformations to conjugate multi-particle symmetry postulates, so as to obtain a twisted realization of the symmetric groups S_n.