Quantization of Yang–Mills theory without the Gribov ambiguity

Abstract

A gauge fixing condition is presented here for non-Abelian gauge theory on the manifold R ⊗ S 1 ⊗ S 1 ⊗ S 1 . It is proved that the new gauge fixing condition is continuous and free from the Gribov ambiguity. While perturbative calculations based on the new gauge condition behave like those based on the axial gauge in ultraviolet region, infrared behaviours of the perturbative series under the new gauge fixing condition are quite nontrivial. The new gauge condition, which reads n · ∂n · A = 0, may not satisfy the boundary condition A µ (∞) = 0 as required by conventional perturbative calculations for gauge theories on the manifold S 4 . However, such contradiction is not harmful for the theory considered here.

A modification of Faddeev–Popov approach free from Gribov ambiguity

“…Besides constraining configuration space to some subset, there are also other ways, for instance, finding a gauge fixing condition which is free from Gribov copies, such as a spacelike planar gauge [33], modified axial gauge [34], and so on. However, such gauge conditions either break the Lorentz invariance or violate the infinite vanishing boundary condition [2,35].…”

A modification of Faddeev-Popov approach free from Gribov ambiguity

“…Besides constraining configuration space to some subset, there are also other ways, for instance, finding a gauge fixing condition which is free from Gribov copies, such as space-like planar gauge [33], modified axial gauge [34], and so on. However, such gauge conditions either break the Lorentz invariance or violate the infinite vanishing boundary condition [2,35].…”