Gribov horizon in Noncommutative QED

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, the standard QED is recovered.