Letters in Mathematical Physics

, Volume 109, Issue 1, pp 187–224 | Cite as

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

  • Ezra GetzlerEmail author


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.


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

Mathematics Subject Classification

70S05 37K05 



I am grateful to Chris Hull for introducing me to the first-order formalism of the spinning particle, and to Si Li, Pavel Mnëv and Sean Pohorence for further insights. This research is partially supported by EPSRC Programme Grant EP/K034456/1 “New Geometric Structures from String Theory”, a Fellowship of the Simons Foundation, and Collaboration Grants #243025 and #524522 of the Simons Foundation. Parts of this paper were written while the author was visiting the Yau Mathematical Sciences Center at Tsinghua University and the Department of Mathematics of Columbia University, as a guest of Si Li and Mohammed Abouzaid, respectively.


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Authors and Affiliations

  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA

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