Algebraic aspects of the background field method

The background field method allows the evaluation of the effective action by exploiting the (background) gauge invariance, which in general yields Ward identities, i.e., linear relations among the vertex functions, In the present approach an extra gauge fixing term is introduced right at the beginning in the action and it is chosen in such a way that BRST invariance is preserved. The background effective action is considered and it is shown to satisfy both the Slavnov-Taylor (ST) identities and the Ward identities. This allows the proof of the background equivalence theorem with the standard techniques. In particular we consider a BRST doublet where the background field enters with a non-zero BRST transformation. The rationale behind the introduction of an extra gauge fixing term is that of removing the singularity of the Legendre transform of the backgound effective action, thus allowing the construction of the connected amplitudes generating functional W-bg. By using the relevant ST identities we show that the functional W-bg-gives the same physical amplitudes as the original one A e started with. Moreover we show that W-bg cannot in general be derived from a classical action by the Gell-Mann-Low formula. As a final point of the paper we show that the BRST doublet generated from the background field does not modify the anomaly of the original underlying gauge theory. The proof is algebraic and makes no use of arguments based on power-counting. (C) 2001 Elsevier Science.