Retarded Functions in Noncommutative Theories

TL;DR

This paper extends the use of retarded functions in quantum field theory to noncommutative settings, identifies issues with unitarity in space-time noncommutativity, and proposes a modified, consistent theory.

Contribution

It introduces a modified noncommutative quantum field theory that maintains unitarity and classical equations of motion at the quantum level.

Findings

Unitarity problems arise in space-time noncommutative theories.

A modified theory restores unitarity and preserves classical equations.

The approach extends retarded functions to noncommutative quantum field theories.

Abstract

The perturbative approach to quantum field theory using retarded functions is extended to noncommutative theories. Unitarity as well as quantized equations of motion are studied and seen to cause problems in the case of space-time noncommutativity. A modified theory is suggested that is unitary and preserves the classical equations of motion on the quantum level.