https://doi.org/10.1140/epjc/s2005-02241-x
theoretical physics
Quantized equations of motion in non-commutative theories
1
Department of Applied Mathematics and Theoretical Physics, Centre of Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge CB3 0WA, UK
2
Institut für Theoretische Physik, Universität Leipzig, Augustusplatz 10/11, 04109, Leipzig, Germany
* e-mail: P.J.Heslop@damtp.cam.ac.uk
Quantum field theories based on interactions which contain the Moyal star product suffer, in the general case when time does not commute with space, from several diseases: quantum equation of motions contain unusual terms, conserved currents cannot be defined and the residual spacetime symmetry is not maintained. All these problems have the same origin: time ordering does not commute with taking the star product. Here we show that these difficulties can be circumvented by a new definition of time ordering: namely with respect to a light-cone variable. In particular the original spacetime symmetries 
and translation invariance turn out to be respected. Unitarity is guaranteed as well.
© Springer-Verlag, 2005
