On kappa-deformation and triangular quasibialgebra structure

TL;DR

This paper demonstrates that the kappa-deformed Poincare algebra can be structured as a triangular quasibialgebra up to a certain order, providing explicit formulas and implications for kappa-deformed quantum field theory.

Contribution

It introduces a triangular quasibialgebra structure to the kappa-deformed Poincare algebra, with explicit R matrix and coassociator calculations up to order 1/kappa^5.

Findings

Explicit R matrix and coassociator up to order 1/kappa^5

Ensures kappa-covariant multi-particle states in quantum field theory

Supports the existence of a universal algebraic structure for kappa-deformation

Abstract

We show that, up to terms of order 1/kappa^5, the kappa-deformed Poincare algebra can be endowed with a triangular quasibialgebra structure. The universal R matrix and coassociator are given explicitly to the first few orders. In the context of kappa-deformed quantum field theory, we argue that this structure, assuming it exists to all orders, ensures that states of any number of identical particles, in any representation, can be defined in a kappa-covariant fashion.