kappa-Deformed Oscillators: Deformed Multiplication Versus Deformed Flip Operator and Multiparticle Clusters

TL;DR

This paper compares two formulations of kappa-deformed oscillator algebra, analyzing their effects on multiparticle states, mass-shell conditions, and field products, revealing nonfactorizable clustering properties.

Contribution

It introduces a transformation from kappa-deformed multiplication to a flip operator formulation, clarifying their impact on multiparticle states and field interactions.

Findings

Kappa-deformed multiplication leads to off-shell oscillators.

Both formulations produce modified mass-shell conditions.

Kappa-deformed star product results in nonfactorizable multiparticle states.

Abstract

We transform the oscillator algebra with kappa-deformed multiplication rule, proposed in [1],[2], into the oscillator algebra with kappa-deformed flip operator and standard multiplication. We recall that the kappa-multiplication of the kappa-oscillators puts them off-shell. We study the explicit forms of modified mass-shell conditions in both formulations: with kappa-multiplication and with kappa-flip operation. On the example of kappa-deformed 2-particle states we study the clustered nonfactorizable form of the kappa-deformed multiparticle states. We argue that the kappa-deformed star product of two free fields leads in similar way to a nonfactorizable kappa-deformed bilocal field. We conclude with general remarks concerning the kappa-deformed n-particle clusters and kappa-deformed star product of n fields.