Eur. Phys. J. C (2003) 31: 129-138
https://doi.org/10.1140/epjc/s2003-01309-y

theoretical physics

Deformed field theory on $\kappa$-spacetime

¹ Fakultät für Physik, Universität München, Theresienstr. 37, 80333, München, Germany
² Max-Planck-Institut für Physik, Föhringer Ring 6, 80805, München, Germany
³ Faculty of Physics, University of Belgrade, Studentski trg 12, 11000, Beograd, Serbia
⁴ Theoretical Physics Division, Rudjer Boskovic Institute, P.O. Box 180, 10002, Zagreb, Croatia

^* e-mail: dmarija@theorie.physik.uni-muenchen.de

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 (the Poincaré group) is replaced by a quantum group. This formalism is demonstrated for the $\kappa$-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. The Dirac and Klein-Gordon equation are defined and an action is found from which they can be derived.