AN EQUIVALENCE PROOF OF THE BACKGROUND GAUGE FIELD QUANTIZATION AND THE CONVENTIONAL ONE

The background gauge field quantization is a convenient tool for study ing 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 theor y, as well as gauge field effective action formulations. We reviewed, to start with, the general formulation and assumptions about this meth od, and we pointed out some critical observations concerning it. In pa rticular, we focus on some of the most common equivalence proofs prese ntly known in the literature. We attempted to give a most convincing d emonstration of this equivalence as it stands between the background g auge field scattering operator and the conventional one. The result sh own here clearly indicates these methods are indeed physically equival ent. In proving that, we neglected all the infrared problems afflictin g the pure Yang-Mills gauge theory; as a matter of fact, they appear t o be a parallel, but nonintersecting problem with respect to the prese nt one, i.e., to prove the equivalence. (C) 1996 American Institute of Physics.