Microlocal Analysis of a Deformed Quantum Field Theory

Abstract

A deformation technique, known as the warped convolution, takes quantum fields in Minkowski spacetime to quantum fields in noncommutative Minkowski space-time. Since a quantum field is an operator valued regular distribution and the warped convolution is (weakly) an oscillatory integral of Rieffel type, we prove that the symbol classes introduced by Hormander admit extensions which are suited to the warped convolutions of scalar quantum field operators. We further show that, if a particular vector state on the undeformed algebra of field operators fulfills the microlocal spectrum condition, then every vector state on the deformed algebra generated by these warped convolutions fulfills the microlocal spectrum condition.