Twist deformations leading to kappa-Poincare Hopf algebra and their application to physics

TL;DR

This paper explores two different twist operators that generate kappa-Poincare Hopf algebra, analyzing their mathematical properties and physical applications such as constructing compatible statistics operators and formulating scalar field theories on deformed spacetime.

Contribution

It introduces and compares two twist operators for kappa-Poincare algebra, one Abelian and one light-like, and applies them to develop deformed quantum field theories and symmetry-compatible operators.

Findings

The light-like twist is expressed solely in terms of Poincare generators.

The Abelian twist extends beyond Poincare algebra into the general linear algebra.

A star product and scalar field theory compatible with kappa-Poincare algebra are constructed.

Abstract

We consider two twist operators that lead to kappa-Poincare Hopf algebra, the first being an Abelian one and the second corresponding to a light-like kappa-deformation of Poincare algebra. The advantage of the second one is that it is expressed solely in terms of Poincare generators. In contrast to this, the Abelian twist goes out of the boundaries of Poincare algebra and runs into envelope of the general linear algebra. Some of the physical applications of these two different twist operators are considered. In particular, we use the Abelian twist to construct the statistics flip operator compatible with the action of deformed symmetry group. Furthermore, we use the light-like twist operator to define a star product and subsequently to formulate a free scalar field theory compatible with kappa-Poincare Hopf algebra and appropriate for considering the interacting phi^4 scalar field model on kappa-deformed space.