Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra

TL;DR

This paper investigates the construction of covariant particle exchange operators in kappa-deformed Poincare symmetric quantum theories, demonstrating their existence for spinless particles and proposing a unique intertwiner based on perturbative analysis.

Contribution

It constructs and analyzes intertwiners for particle exchange in kappa-deformed Poincare algebra, introducing a conjecture on their uniqueness and existence for spinless particles.

Findings

Intertwiners exist for spinless particles in kappa-deformed theories.

Perturbative calculations support a unique preferred intertwiner.

Conjecture on the existence and uniqueness of the intertwiner.

Abstract

To speak about identical particles - bosons or fermions - in quantum field theories with kappa-deformed Poincare symmetry, one must have a kappa-covariant notion of particle exchange. This means constructing intertwiners of the relevant representations of kappa-Poincare. We show, in the simple case of spinless particles, that intertwiners exist, and, supported by a perturbative calculation to third order in 1/kappa, make a conjecture about the existence and uniqueness of a certain preferred intertwiner defining particle exchange in kappa-deformed theories.