Kappa-Minkowski space-time and the star product realizations

TL;DR

This paper explores different realizations of $appa$-deformed Minkowski space, constructs corresponding star products, and develops a scalar field theory that is equivalent to a nonlocal relativistic theory on ordinary Minkowski space.

Contribution

It introduces multiple realizations of $appa$-Minkowski space, derives their star products, and formulates a scalar field theory equivalent to a nonlocal relativistic theory.

Findings

Multiple realizations of $appa$-Minkowski space are identified.

Star products are explicitly constructed for each realization.

Scalar field theory on $appa$-space is shown to be equivalent to a nonlocal theory on Minkowski space.

Abstract

We investigate a Lie algebra-type $ \kappa$-deformed Minkowski space-time with undeformed Lorentz algebra and mutually commutative vector-like Dirac derivatives. There are infinitely many realizations of $ \kappa$-Minkowski space. The coproduct and the star product corresponding to each of them are found. Utilizing the properties of the {\em{natural}} realization, we construct a scalar field theory on $ \kappa$-deformed Minkowski space and show that it is equivalent to the scalar, nonlocal, relativistically invariant field theory on the ordinary Minkowski space.