$\kappa$--deformed Wigner construction of relativistic wave functions and free fields on $\kappa$-Minkowski space

TL;DR

This paper extends Wigner's representation theory to the $kappa$-deformed Poincaré group, describing free fields on noncommutative $kappa$-Minkowski space, including Klein-Gordon, Dirac, Proca, and Maxwell fields.

Contribution

It introduces a $kappa$-deformed Wigner construction for relativistic wave functions and free fields on noncommutative space-time, expanding the mathematical framework of quantum field theory.

Findings

Wave functions satisfy free field equations on $kappa$-deformed Minkowski space.

Explicit treatment of Klein-Gordon, Dirac, Proca, and Maxwell fields.

Discussion of aspects of second quantization in the deformed setting.

Abstract

We describe the extension of the Wigner`s infinite-dimensional unitary representations of Poincar\'{e} group to the case of $\kappa$-deformed Poincar\'{e} group. We show that the corresponding coordinate wave functions on noncommutative space-time are described by free field equations on $\kappa$-deformed Minkowski space. The cases of Klein--Gordon, Dirac, Proca and Maxwell fields are considered. Finally some aspects of second quantization are also discussed.