Equivalence between the gauge n ⋅ ∂n ⋅ A = 0 and the axial gauge

• Published in: Nuclear physics. B 2022-07, Vol.980, p.115813, Article 115813
• Main Authors: Zhou, Gao-Liang, Yan, Zheng-Xin, Zhang, Xin
• Format: Article
• Language: English
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/j.nuclphysb.2022.115813

Singularity of the gauge condition n⋅∂n⋅A=0 at n⋅k=0 is studied here. Such singularity is different from that in axial gauge and can not be regularized through analytical continuation method. It is proved that construction of continuous and well defined gauge links is obstructed by the Gribov ambiguity. Thus continuous gauge conditions which are free from the Gribov ambiguity are essential in studies on nonlocal gauge invariant objects. The Faddeev-Popov determinant of the gauge n⋅∂n⋅A=0, which is solved explicitly here, behaves like a δ-functional of gauge potentials once singularities in the functional integral is neglected and the length of the space along nμ direction tends to infinity. As a sequence, perturbation series in the gauge n⋅∂n⋅A=0 are equivalent to those in axial gauge for objects which are free from these singularities. However, the equivalence between the gauge n⋅∂n⋅A=0 and axial gauge is nontrivial for objects suffering from these singularities. It is also demonstrated through explicit calculations that the equivalence for long distance objects is not the case in general, especially lattice calculations show significant distinctions among the axial gauge n⋅A=0, the Landau gauge ∂⋅A=0 and the gauge n⋅∂n⋅A=0 for long distance objects.