Non-trivial Backgrounds in (non-perturbative) Yang-Mills Theory by the Slavnov-Taylor Identity

Abstract

We show that in the background field method (BFM) quantization of Yang-Mills theory the dependence of the vertex functional on the background field is controlled by a canonical transformation w.r.t. the Batalin-Vilkovisky bracket, naturally associated with the BRST symmetry of the theory. Since it only relies on the Slavnov-Taylor identity of the model, this result holds both in perturbation theory and in the non-perturbative regime. It provides a general consistent framework for the systematic implementation of the BFM in non-perturbative approaches to QCD, like e.g. those based on the Schwinger-Dyson equations or the lattice, in the presence of topologically non-trivial background configurations. The analysis is carried out in an arbitrary (background) R_ξ-gauge.

References added. RevTeX, 15 pages. Contributed to Quantum Theory and Symmetries 7, August 7-13, 2011, Prague

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Cited by in corpus (1)

• Background field dependence from the Slavnov-Taylor identity in (non-perturbative) Yang-Mills theory