Relational Symplectic Groupoid Quantization for Constant Poisson Structures

Abstract

As a detailed application of the BV-BFV formalism for the quantization of field theories on manifolds with boundary, this note describes a quantization of the relational symplectic groupoid for a constant Poisson structure. The presence of mixed boundary conditions and the globalization of results is also addressed. In particular, the paper includes an extension to space-times with boundary of some formal geometry considerations in the BV-BFV formalism, and specifically introduces into the BV-BFV framework a "differential" version of the classical and quantum master equations. The quantization constructed in this paper induces Kontsevich's deformation quantization on the underlying Poisson manifold, i.e., the Moyal product, which is known in full details. This allows focussing on the BV-BFV technology and testing it. For the unexperienced reader, this is also a practical and reasonably simple way to learn it.

32 pages, 15 figures, some changes (including the correction of a minor mistake) included; new appendix with the explicit computations added; to appear in Lett. Math. Phys

References in corpus (1)

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Cited by in corpus (5)

• Introduction to the BV-BFV formalism
• Globalization for Perturbative Quantization of Nonlinear Split AKSZ Sigma Models on Manifolds with Boundary
• On the Globalization of the Poisson Sigma Model in the BV-BFV Formalism
• Formal Global Perturbative Quantization of the Rozansky-Witten Model in the BV-BFV Formalism
• Convolution algebras for Relational Groupoids and Reduction