Local Field Theory ON $\kappa$-Minkowski Space, Star Products and Noncommutative Translations

TL;DR

This paper develops a local field theory framework on $$-deformed Minkowski space, providing explicit star product formulas and linking noncommutative translations to standard translations, advancing understanding of noncommutative geometry in field theory.

Contribution

It introduces explicit star product formulas for $$-deformed Minkowski space and relates noncommutative translations to commutative ones, enhancing the mathematical tools for noncommutative field theories.

Findings

Explicit star product formulas for $$-deformed Minkowski space.

Representation of noncommutative translations via standard translations.

Analysis of reality conditions and deformation of action functionals.

Abstract

We consider local field theory on $\kappa$-deformed Minkowski space which is an example of solvable Lie-algebraic noncommutative structure. Using integration formula over $\kappa$-Minkowski space and $\kappa$-deformed Fourier transform we consider for deformed local fields the reality conditions as well as deformation of action functionals in standard Minkowski space. We present explicite formulas for two equivalent star products describing CBH quantization of field theory on $\kappa$-Minkowski space. We express also via star product technique the noncommutative translations in $\kappa$-Minkowski space by commutative translations in standard Minkowski space.