Field theory on Kappa-spacetime

Abstract

A general formalism is developed, that allows the construction of field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime is replaced by a quantum group. This formalism is demonstrated for the κ-deformed Poincaré algebra and its quantum space. The algebraic setting is mapped to the algebra of functions of commuting variables with a suitable *-product. Fields are elements of this function algebra. As an example, the Klein-Gordon equation is defined and derived from an action.