On the quantum Batalin-Vilkovisky formalism and the renormalization of non linear symmetries

Abstract

The most convenient tool to study the renormalization of a Lagrangian field theory invariant under non linear local or global symmetries is the proper solution to the master equation of the extended antifield formalism. It is shown that, from the knowledge of the BRST cohomology, it is possible to explicitly construct a further extension of the formalism containing all the observables of the theory and satisfying an extended master equation, with some of the features of the quantum Batalin-Vilkovisky master equation already present at the classical level. This solution has the remarkable property that all its infinitesimal deformations can be extended to complete deformations. The deformed solutions differs from the original one through the addition of terms related to coupling constant and anticanonical field-antifield redefinitions. As a consequence, all theories admitting an invariant regularization scheme are shown to be renormalizable while preserving the symmetries, in the sense that both the subtracted and the effective action satisfy the extended master equation, and this independently of power counting restrictions. The anomalous case is also studied and a suitable definition of the Batalin-Vilkovisky ``Delta'' operator in the context of dimensional renormalization is proposed.