Perturbative quantum gauge theories on manifolds with boundary

Abstract

This paper introduces a general perturbative quantization scheme for gauge theories on manifolds with boundary, compatible with cutting and gluing, in the cohomological symplectic (BV-BFV) formalism. Explicit examples, like abelian BF theory and its perturbations, including nontopological ones, are presented.

Ver. 2: Improved presentation, especially we added a detailed discussion of the space of states. To appear in Commun. Math. Phys

References in corpus (4)

• Hunt for new phenomena using large jet multiplicities and missing transverse momentum with ATLAS in 4.7 fb^-1 of sqrt(s) = 7 TeV proton-proton collisions
• Split Chern-Simons theory in the BV-BFV formalism
• Gluing Manifolds in the Cahiers Topos
• Discrete BF theory

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