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.
Highlights
The occurrence of so-called Gribov ambiguities for Yang-Mills theories was first discussed in [1], where Gribov showed that for non-Abelian gauge theories on flat topologically trivial spacetimes, gauge fixing is problematic
Gribov ambiguity amounts to the fact that there are in general different field configurations which obey the same gauge-fixing condition, but which are related by a gauge transformation, i.e., they are on the same gauge orbit
For Quantum Chromodynamics (QCD), Gribov copies pose a real threat to the accurate description of the low-energy regime of the theory, the gauge group of SU(N) Yang-Mills theories being nontrivial for N ≥ 2
Summary
The occurrence of so-called Gribov ambiguities for Yang-Mills theories was first discussed in [1], where Gribov showed that for non-Abelian gauge theories on flat topologically trivial spacetimes, gauge fixing is problematic. As first shown by Singer [2] and independently by Narasimhan and Ramadas [3], this occurrence can be given a precise mathematical characterisation in terms of topological non-triviality of G, the pertinent gauge group involved. Following the same approach as in non-Abelian gauge theories [7], the ensuing constraint on the physical space of connections is implemented by requiring that the ghost propagator does not develop poles. This implies a modification of the photon propagator.
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