A short introduction to $\kappa$-deformation

TL;DR

This paper reviews $ppa$-deformation, exploring algebraic and geometric aspects of $ppa$-Poincare9 algebra, and constructs free scalar field theories on non-commutative $ppa$-Minkowski space and curved momentum space.

Contribution

It provides a concise overview of $ppa$-deformation, including algebraic, geometric, and field theory constructions, highlighting recent developments.

Findings

Constructed free scalar field theory on $ppa$-Minkowski space

Developed scalar field theory on curved momentum space

Discussed potential for interacting scalar fields

Abstract

In this short review we describe some aspects of $\kappa$-deformation. After discussing the algebraic and geometric approaches to $\kappa$-Poincar\'e algebra we construct the free scalar field theory, both on non-commutative $\kappa$-Minkowski space and on curved momentum space. Finally, we make a few remarks concerning interacting scalar field.