# The Gribov problem in Noncommutative gauge theory

## TL;DR

This paper demonstrates that noncommutative QED exhibits a Gribov ambiguity similar to non-Abelian gauge theories, revealing a novel geometric effect absent in the commutative case.

## Contribution

It shows that noncommutative geometry induces Gribov copies in Abelian gauge theories, a phenomenon previously thought exclusive to non-Abelian cases.

## Key findings

- Identifies infinite solutions for Gribov copies in noncommutative QED.
- Shows the effect vanishes as noncommutative parameter approaches zero.
- Highlights a new geometric feature unique to noncommutative gauge theories.

## Abstract

After reviewing Gribov ambiguity of non-Abelian gauge theories, a phenomenon related to the topology of the bundle of gauge connections, we show that there is a similar feature for noncommutative QED over Moyal space, despite the structure group being Abelian, and we exhibit an infinite number of solutions for the equation of Gribov copies. This is a genuine effect of noncommutative geometry which disappears when the noncommutative parameter vanishes.