Deformed Field Theory on kappa-spacetime

TL;DR

This paper develops a formalism for constructing field theories on quantum-deformed spacetimes, specifically demonstrating it for kappa-deformed Poincaré algebra, replacing classical symmetries with quantum groups.

Contribution

It introduces a general method to formulate field theories on quantum spaces with deformed symmetries, exemplified by the kappa-deformed Poincaré algebra and its associated quantum space.

Findings

Defined Dirac and Klein-Gordon equations on kappa-spacetime

Constructed an action principle for fields on deformed spacetime

Mapped algebraic structures to functions with star-products

Abstract

A general formalism is developed that allows the construction of a field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime (Poincar\' e group) is replaced by a quantum group. This formalism is demonstrated for the kappa-deformed Poincar\'e algebra and its quantum space. The algebraic setting is mapped to the algebra of functions of commuting variables with a suitable star-product. Fields are elements of this function algebra. The Dirac and Klein-Gordon equation are defined and an action is found from which they can be derived.