Covariance in the Batalin–Vilkovisky formalism and the Maurer–Cartan equation for curved Lie algebras

Ezra Getzler*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We express covariance of the Batalin–Vilkovisky formalism in classical mechanics by means of the Maurer–Cartan equation in a curved Lie superalgebra, defined using the formal variational calculus and Sullivan’s Thom–Whitney construction. We use this framework to construct a Batalin–Vilkovisky canonical transformation identifying the Batalin–Vilkovisky formulation of the spinning particle with an AKSZ field theory.

Original languageEnglish (US)
Pages (from-to)187-224
Number of pages38
JournalLetters in Mathematical Physics
Volume109
Issue number1
DOIs
StatePublished - Jan 10 2019

Keywords

  • Batalin–Vilkovisky field theory
  • Spinning particle
  • Supergravity
  • Thom–Whitney normalization
  • Variational calculus

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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