The Gribov problem in noncommutative QED

Abstract

It is shown that in the noncommutative version of QED (NCQED) Gribov copies induced by the noncommutativity of space-time appear in the Landau gauge. This is a genuine effect of noncommutative geometry which disappears when the noncommutative parameter vanishes.

Spectral Noncommutative Geometry Standard Model and all that

“…These beta functions, generally speaking, depend on all the coupling constants, which are involved in the model and can be computed in a perturbative way via the loop expansion [98][99][100]. At the one loop approximation the beta functions for the gauge couplings are given by 29) therefore at this approximation the system (2.28) is closed, and moreover the three equations are not coupled with each other. The initial conditions for these equations are can be taken from the experiment, in particular at µ = M Z : Using the results of [98][99][100] one can check that the two loop corrections that do not change this plot significantly.…”

Noncommutative Geometry and Particle Physics

“…A possible basis for the 1-forms is then given by 3 eδ e , (1 − e)δ (1 − e) , (A. 22) and their values are The geometry in this case is almost commutative, i.e. the product of the ordinary commutative manifold times a finite dimensional space composed by two points.…”

The Gribov problem in noncommutative gauge theory

“…Let us come to the physical configuration space B = A/G. Since A is homotopically trivial whereas B and G in general aren't, 4 A cannot be globally trivialized as the product of B and G unless G is topologically trivial. On the basis of (2.19), both G and B are only trivial for G = U (1), which is the case for electrodynamics.…”

“…A less investigated problem is the problem of Gribov ambiguity. Indeed it has been shown [4] that noncommutative QED similarly to commutative non-Abelian gauge theories, exhibits Gribov copies. For a review of noncommutative gauge theories see [27] and refs.…”

“…We thus analyze the equation for Gribov copies for noncommutative U (1) gauge theory. The latter is based on the results obtained in [4].…”