Light-like $\kappa$-deformations and scalar field theory via Drinfeld twist

TL;DR

This paper develops a scalar field theory on light-like $appa$-deformed Minkowski space using Drinfeld twists, showing the equivalence to standard theories and addressing integration and interaction issues.

Contribution

It introduces a new approach to formulating scalar field theories on $appa$-deformed space via Drinfeld twists, ensuring compatibility with $appa$-Poincare9-Hopf algebra.

Findings

The star-product allows defining scalar fields on $appa$-Minkowski space without new measures.

The free scalar field theory is equivalent to a commutative theory on Minkowski space.

The paper discusses a compatible interacting $phi^4$ model.

Abstract

In this article we will use the Drinfeld twist leading to light-like $\kappa$-deformations of Poincar\'e algebra. We shall apply the standard Hopf algebra methods in order to define the star-product, which shall be used to formulate a scalar field theory compatible with $\kappa$-Poincar\'e-Hopf algebra. Using this approach we show that there is no problem with formulating integration on $\kappa$-Minkowski space and no need for introducing a new measure. We have shown that the $\star$-product obtained from this twist enables us to define a free scalar field theory on $\kappa$-Minkowski space that is equivalent to a commutative one on a usual Minkowski space. We also discuss the interacting $\phi^4$ scalar field model compatible with $\kappa$-Poincar\'e-Hopf algebra.