Classical BV Theories on Manifolds with Boundary

2012/01/31 by Alberto S. Cattaneo, Aberto S. Cattaneo, Pavel Mnev +1 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Boundary (topology) #Codimension #Extension (predicate logic) #Gauge theory #Global analysis #M-theory #Manifold (fluid mechanics) #Noncommutative and Quantum Gravity Theories #Poisson manifold #Quantization (signal processing) #Spacetime #hep-th #math-ph #math.MP

paper · pdf · doi:10.1007/s00220-014-2145-3

published as Commun. Math. Phys. 332, 535-603 (2014) · The second version has many typos corrected, references added. Some typos are probably still there, in particular, signs in examples. In the third version more typoes are corrected and the exposition is slightly changed

arxiv created 2012/06/28 · openalex publication_date 2014/08/28 · openalex created_date 2019/06/27 · arxiv updated 2020/02/03 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• Quantum field theory and the Jones polynomial
• Higher-dimensional algebra and topological quantum field theory
• Invariants of 3-manifolds via link polynomials and quantum groups
• A Path Integral Approach¶to the Kontsevich Quantization Formula
• Renormalization of gauge theories
• Two Dimensional Gauge Theories Revisited
• Classical and quantum conformal field theory
• On the Classification of Topological Field Theories

Cited by

• Split Chern-Simons theory in the BV-BFV formalism
• Homotopy Algebras in String Field Theory
• BV equivalence between triadic gravity and BF theory in three dimensions
• The Reduced Phase Space of Palatini–Cartan–Holst Theory

Related

• Perturbative BV theories with Segal-like gluing
• Perturbative quantum gauge theories on manifolds with boundary
• Degenerate Classical Field Theories and Boundary Theories
• Canonical Structure of Field Theories with Boundaries and Applications to Gauge Theories
• Covariant Hamiltonian Field Theories on Manifolds with Boundary:\n Yang-Mills Theories