A critical analysis is given in order to set up a well-defined perturbative expansion for Yang-Mills Euclidean theories within the axial gauge choice, using Cauchy principal value prescription to handle the spurious singularities. It is shown that, following a mathematically meaningful and unambiguous procedure, the exponential behavior of the Euclidean Wilson loop does not occur at variance with the covariant and planar gauge choices. A comparison with previous similar approaches and results is worked out in order to clearly understand the reasons for the breakdown of gauge invariance in the present case. In particular we can conclude that the so far proposed alternative prescriptions, which have been claimed to restore gauge invariance, should be carefully reexamined, at least for the Euclidean formulation.
- axial gauge
- wilson loop