  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 can not 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 SO(1,1) x
SO(2) and translation invariance turn out to be respected. Unitarity is
guaranteed as well.

High Energy Physics - Theory