Unitarity of Time-Like Noncommutative Gauge Theories: The Violation of Ward Identities in Time-Ordered Perturbation Theory

TL;DR

This paper investigates the violation of Ward identities in time-like noncommutative gauge theories using time-ordered perturbation theory, revealing fundamental issues with unitarity in these models.

Contribution

It demonstrates that Ward identities cannot be maintained at all orders in noncommutativity parameters, highlighting unitarity problems in time-ordered approaches.

Findings

Ward identities are violated at all orders in noncommutativity parameters.

Time-ordered perturbation theory cannot resolve unitarity issues in time-like noncommutative gauge theories.

Fundamental limitations are identified in applying standard perturbative methods to these theories.

Abstract

We study Ward identities for simple processes with external gauge bosons in the time-ordered perturbation theory approach to time-like noncommutative gauge theories. We demonstrate that these Ward identities cannot be satisfied when all orders in the noncommutativity parameters theta_i0 are taken into account. We conclude that in time-ordered perturbation theory one cannot solve the unitarity problem of time-like noncommutative quantum field theories.