Scalar Field theory in $\kappa$-Minkowski spacetime from twist

TL;DR

This paper constructs a free scalar field theory in four-dimensional $ k$-Minkowski spacetime using twist deformation of the linear diffeomorphism group, resulting in an action similar to the commutative case.

Contribution

It introduces a novel approach to defining scalar fields in $ k$-Minkowski spacetime via twist deformation of $U(igl(4,R))$, connecting noncommutative geometry with field theory.

Findings

The action differs from the commutative case only in the integration measure.

The scalar field theory is explicitly constructed in four dimensions.

The approach links twist deformation with scalar field dynamics in noncommutative spacetime.

Abstract

Using the twist deformation of $U(igl(4,R))$, the linear part of the diffeomorphism, we define a scalar function and construct a free scalar field theory in four-dimensional $\kappa$-Minkowski spacetime. The action in momentum space turns out to differ only in integration measure from the commutative theory.