Batalin-Vilkovisky Integrals in Finite Dimensions
Carlo Albert, Bea Bleile, J\"urg Fr\"ohlich
TL;DR
This paper explores the Batalin-Vilkovisky (BV) method for analyzing finite-dimensional integrals with gauge symmetries, introducing homological perturbation theory to develop the BV integration framework and discuss localization and anomalies.
Contribution
It introduces homological perturbation theory into BV integration and applies it to finite-dimensional systems, expanding the understanding of localization and anomalies in this context.
Findings
Develops BV integration theory using homological perturbation theory.
Demonstrates localization techniques within BV framework.
Discusses handling of anomalous symmetries in BV integrals.
Abstract
The Batalin-Vilkovisky method (BV) is the most powerful method to analyze functional integrals with (infinite-dimensional) gauge symmetries presently known. It has been invented to fix gauges associated with symmetries that do not close off-shell. Homological Perturbation Theory is introduced and used to develop the integration theory behind BV and to describe the BV quantization of a Lagrangian system with symmetries. Localization (illustrated in terms of Duistermaat-Heckman localization) as well as anomalous symmetries are discussed in the framework of BV.
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