Communications in Mathematical Physics

, Volume 332, Issue 2, pp 535–603 | Cite as

Classical BV Theories on Manifolds with Boundary

  • Alberto S. Cattaneo
  • Pavel Mnev
  • Nicolai ReshetikhinEmail author


In this paper we extend the classical BV framework to gauge theories on spacetime manifolds with boundary. In particular, we connect the BV construction in the bulk with the BFV construction on the boundary and we develop its extension to strata of higher codimension in the case of manifolds with corners. We present several examples including electrodynamics, Yang-Mills theory and topological field theories coming from the AKSZ construction, in particular, the Chern-Simons theory, the BF theory, and the Poisson sigma model. This paper is the first step towards developing the perturbative quantization of such theories on manifolds with boundary in a way consistent with gluing.


Manifold Symplectic Form Smooth Point Ghost Number Spacetime Manifold 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Alberto S. Cattaneo
    • 1
  • Pavel Mnev
    • 1
  • Nicolai Reshetikhin
    • 2
    Email author
  1. 1.Institut für MathematikUniversität ZürichZurichSwitzerland
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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