Unitary Quantum Field Theory on the Noncommutative Minkowski space

TL;DR

This paper discusses issues of unitarity violation in quantum field theory on noncommutative Minkowski space and proposes alternative approaches to preserve unitarity, with insights into recent developments.

Contribution

It introduces alternative formulations of quantum field theory on noncommutative spacetime that avoid unitarity violation caused by modified Feynman rules.

Findings

Violation of unitarity linked to time ordering in perturbation theory

Proposes alternative approaches that preserve unitarity

Provides an outlook on recent related work

Abstract

This is the written version of a talk I gave at the 35th Symposium Ahrenshoop in Berlin, Germany, August 2002. It is an exposition of joint work with S. Doplicher, K. Fredenhagen, and Gh. Piacitelli [1]. The violation of unitarity found in quantum field theory on noncommutative spacetimes in the context of the so-called modified Feynman rules is linked to the notion of time ordering implicitely used in the assumption that perturbation theory may be done in terms of Feynman propagators. Two alternative approaches which do not entail a violation of unitarity are sketched. An outlook upon our more recent work is given.