Kappa-deformed oscillators, the choice of star product and free kappa-deformed quantum fields

TL;DR

This paper explores different approaches to constructing free kappa-deformed quantum fields with c-number commutators, analyzing the effects of star product choices and mass-shell modifications on the oscillator algebra and field properties.

Contribution

It introduces a new concept of kappa-deformed oscillator algebra and examines how different star product modifications influence the construction of free kappa-deformed quantum fields.

Findings

Standard kappa-star product does not yield free fields with c-number commutators.

Modified kappa-star product allows a broad class of kappa-deformed statistics with c-number commutators.

The structure of kappa-deformed oscillators depends on the choice of star product and mass-shell conditions.

Abstract

In order to obtain free kappa-deformed quantum fields (with c-number commutators) we proposed new concept of kappa-deformed oscillator algebra [1] and the modification of kappa-star product [2], implementing in the product of two quantum fields the change of standard kappa-deformed mass-shell conditions. We recall here that the kappa-deformed oscillators recently introduced in [3]-[5] lie on standard kappa-deformed mass-shell. Firstly, we study kappa-deformed fields with the standard kappa-star product, what implies that in the oscillator algebra the corresponding kappa-deformed oscillators lie on standard kappa-deformed mass-shell. We argue that for the kappa-deformed algebra of such field oscillators which carry fourmomenta on kappa-deformed mass-shell it is not possible to obtain the free quantum kappa-deformed fields with the c-number commutators. Further, we study kappa-deformed quantum fields with the modified kappa-star product which implies the modification of kappa-deformed mass-shell. We obtain large class of kappa-deformed statistics depending on six arbitrary functions which provides the c-number field commutator functions. Such general class of kappa-oscillators can be described as the kappa-deformation of standard oscillator algebra obtained by composing general kappa-deformed multiplication with the deformation of the flip operator.