Microlocal Analysis of a Deformed Quantum Field Theory

TL;DR

This paper investigates how a deformation method called warped convolution affects quantum fields in Minkowski spacetime, showing that certain spectral conditions are preserved under this deformation.

Contribution

It demonstrates that symbol classes for quantum fields extend to warped convolutions and that microlocal spectrum conditions are maintained after deformation.

Findings

Symbol classes extend to warped convolutions of scalar quantum fields.

Microlocal spectrum condition is preserved under deformation.

Warped convolution maintains key spectral properties of quantum fields.

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.