Covariant particle exchange for kappa-deformed theories in 1+1 dimensions

TL;DR

This paper explores how identical scalar particles exchange in 1+1 dimensional theories with kappa-deformed Poincare symmetry, revealing a unique, covariant intertwiner that governs particle exchange.

Contribution

It demonstrates the realization of the symmetric group on N-particle states in a kappa-covariant manner, with a unique intertwiner for two particles that squares to identity.

Findings

The symmetric group can be realized covariantly in 1+1 dimensions.

There is a unique non-trivial intertwiner for two particles.

The intertwiner automatically squares to the identity.

Abstract

We consider the exchange of identical scalar particles in theories with kappa-deformed Poincare symmetry. We argue that, at least in 1+1 dimensions, the symmetric group S_N can be realized on the space of N-particle states in a kappa-covariant fashion. For the case of two particles this realization is unique: we show that there is only one non-trivial intertwiner, which automatically squares to the identity.