Batalin-Vilkovisky Integrals in Finite Dimensions

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.

35 pages

References in corpus (4)

• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• On the origin of the BV operator on odd symplectic supermanifolds
• Renormalisation and the Batalin-Vilkovisky formalism
• Noether's variational theorem II and the BV formalism

Cited by in corpus (9)

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• Correlation functions on the lattice and twisted cocycles
• Non-perturbative computation of lattice correlation functions by differential equations
• Homological perturbation theory for nonperturbative integrals
• Lagrangian Relations and Quantum $L_{\infty }$ Algebras
• A topological quantum field theory for $\mathrm{Spin}(7)$-instantons