An equivalence proof of the background gauge field quantization and the conventional one

Abstract

The background gauge field quantization is a convenient tool for studying weakly interacting gauge and matter fields or analyzing anomalous current conservation in fermionic structures. This method is from the mid 1970’s, but it is only today that it received renewed interest for investigating nonperturbative evolution equations in Yang–Mills theory, as well as gauge field effective action formulations. We reviewed, to start with, the general formulation and assumptions about this method, and we pointed out some critical observations concerning it. In particular, we focus on some of the most common equivalence proofs presently known in the literature. We attempted to give a most convincing demonstration of this equivalence as it stands between the background gauge field scattering operator and the conventional one. The result shown here clearly indicates these methods are indeed physically equivalent. In proving that, we neglected all the infrared problems afflicting the pure Yang–Mills gauge theory; as a matter of fact, they appear to be a parallel, but nonintersecting problem with respect to the present one, i.e., to prove the equivalence.