Quons in Relativistic Theories Must be Bosons or Fermions

TL;DR

This paper demonstrates that in relativistic quantum theories, particles described by quon algebra are restricted to being either bosons or fermions, despite the algebra's interpolation parameter.

Contribution

It proves that relativistic constraints force quons to behave as either bosons or fermions, limiting the algebra's interpolation in such theories.

Findings

Quons are restricted to bosonic or fermionic statistics in relativistic theories.

Derived conservation of statistics relations for quons.

Showed that the interpolation parameter q cannot produce new particle types in relativistic contexts.

Abstract

The quon algebra describes particles, ``quons,'' that are neither fermions nor bosons using a label q that parametrizes a smooth interpolation between bosons (q = +1) and fermions (q = -1). We derive ``conservation of statistics'' relations for quons in relativistic theories, and show that in relativistic theories quons must be either bosons or fermions.