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BV equivalence with boundary.
Simão, F M Castela; Cattaneo, A S; Schiavina, M.
Afiliação
  • Simão FMC; Queen Mary University of London, School of Mathematical Sciences, Mile End Rd, London, E1 4NS UK.
  • Cattaneo AS; Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland.
  • Schiavina M; Institute for Theoretical Physics and Department of Mathematics, ETH Zurich, Rämistrasse 101, 8092 Zürich, Switzerland.
Lett Math Phys ; 113(1): 25, 2023.
Article em En | MEDLINE | ID: mdl-36845409
An extension of the notion of classical equivalence of equivalence in the Batalin-Vilkovisky (BV) and Batalin-Fradkin-Vilkovisky (BFV) frameworks for local Lagrangian field theory on manifolds possibly with boundary is discussed. Equivalence is phrased in both a strict and a lax sense, distinguished by the compatibility between the BV data for a field theory and its boundary BFV data, necessary for quantisation. In this context, the first- and second-order formulations of nonabelian Yang-Mills and of classical mechanics on curved backgrounds, all of which admit a strict BV-BFV description, are shown to be pairwise equivalent as strict BV-BFV theories. This in particular implies that their BV complexes are quasi-isomorphic. Furthermore, Jacobi theory and one-dimensional gravity coupled with scalar matter are compared as classically equivalent reparametrisation-invariant versions of classical mechanics, but such that only the latter admits a strict BV-BFV formulation. They are shown to be equivalent as lax BV-BFV theories and to have isomorphic BV cohomologies. This shows that strict BV-BFV equivalence is a strictly finer notion of equivalence of theories.
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Texto completo: 1 Coleções: 01-internacional Base de dados: MEDLINE Idioma: En Ano de publicação: 2023 Tipo de documento: Article

Texto completo: 1 Coleções: 01-internacional Base de dados: MEDLINE Idioma: En Ano de publicação: 2023 Tipo de documento: Article