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

TL;DR

This paper develops an extended quantum Batalin-Vilkovisky formalism to analyze the renormalization of theories with non-linear symmetries, ensuring symmetry preservation and renormalizability through cohomological methods.

Contribution

It introduces a new extension of the antifield formalism incorporating all observables, enabling explicit construction of solutions satisfying an extended master equation at the classical level.

Findings

The formalism guarantees all infinitesimal deformations extend to full deformations.

The approach proves theories with invariant regularization are renormalizable while preserving symmetries.

A new definition of the BV ``Delta'' operator for dimensional renormalization is proposed.

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.