The classical master equation (with an appendix by Tomer M. Schlank)
type: Item
instance of: scholarly article
zbMATH Open document ID: 1304.81144
publication date: 2014-08-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1212.1631
Mathematics Subject Classification ID: 81T70
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 81Q30
Mathematics Subject Classification ID: 14F43
Mathematics Subject Classification ID: 17B63
Mathematics Subject Classification ID: 81S22
zbMATH DE Number: 6329441
zbMATH Keywords: classical master equation
zbMATH Keywords: affine varieties
zbMATH Keywords: stable equivalence
zbMATH Keywords: BRST cohomology
zbMATH Keywords: Poisson\({}_0\)-algebras
zbMATH Keywords: Lie-Rinehart algebra
zbMATH Keywords: critical locus
zbMATH Keywords: quasi-projective varieties
zbMATH Keywords: open affine cover
author: Giovanni Felder
author: David Kazhdan
MaRDI profile type: Publication
arXiv ID: 1212.1631
arXiv classification: math.AG
arXiv classification: math-ph
arXiv classification: math.DG
arXiv classification: math.MP
title: The classical master equation (with an appendix by Tomer M. Schlank)
review text: The authors formalize the construction by \textit{I. A. Batalin} and \textit{G. A. Vilkovisky} [``Gauge algebra and quantization'', Phys. Lett. B 102, No. 1, 27--31 (1981; \url{doi:10.1016/0370-2693(81)90205-7}), ``Quantization of gauge theories with linearly dependent generators'', Phys. Rev. D (3) 28, No. 10, 2567--2582 (1983; \url{doi:10.1103/PhysRevD.28.2567})] of a solution of the classical master equation associated with a regular function on a nonsingular affine variety (the classical action). The notion of stable equivalence of solutions is introduced, and it is proven that a solution exists and is unique up to stable equivalence. A consequence is that the associated BRST cohomology, with its structure of Poisson\({}_0\)-algebra, is independent of choices and is uniquely determined up to unique isomorphism by the classical action. It is also given a geometric interpretation of the BRST cohomology sheaf in degree 0 and 1 as the cohomology of a Lie-Rinehart algebra associated with the critical locus of the classical action. Finally it is considered the case of a quasi-projective varieties and it is shown that the BRST sheaves defined on an open affine cover can be glued to a sheaf of differential Poisson\({}_0\)-algebras.NEWLINENEWLINEFor the entire collection see [Zbl 1285.00037].
reviewed by: Vladimir Balan
description: scientific article; zbMATH DE number 6329441