Gribov horizon in Noncommutative QED

TL;DR

This paper investigates the Gribov ambiguity in Noncommutative QED, establishing conditions to avoid ghost propagator poles and deriving a modified photon propagator dependent on non-commutativity.

Contribution

It introduces a positive Faddeev-Popov operator and implements the Gribov no-pole condition in NCQED, extending the understanding of gauge fixing ambiguities in noncommutative gauge theories.

Findings

Derived the photon propagator in NCQED with non-commutativity dependence

Established the Gribov no-pole condition for NCQED

Recovered standard QED in the commutative limit

Abstract

It is known that Noncommutative QED (NCQED) exhibits Gribov ambiguities in the Landau gauge. These ambiguities are related to zero modes of the Faddeev-Popov operator and arise in the ghost propagator when it has a pole. In this work, we establish a positive Faddeev-Popov operator for NCQED and the condition for the ghost propagator not to have poles, the so-called Gribov no-pole condition. This condition is implemented in the path integral, and allows for the calculation of the photon propagator in momentum space, which is dependent on the squared non-commutativity parameter. In the commutative limit standard QED is recovered.