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Relational symplectic groupoid quantization for constant poisson structures


Cattaneo, Alberto Sergio; Moshayedi, Nima; Wernli, Konstantin (2017). Relational symplectic groupoid quantization for constant poisson structures. Letters in Mathematical Physics, 107(9):1649-1688.

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 are 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 inexperienced reader, this is also a practical and reasonably simple way to learn it.

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 are 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 inexperienced reader, this is also a practical and reasonably simple way to learn it.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:31 September 2017
Deposited On:24 Jan 2018 14:19
Last Modified:28 Apr 2018 00:00
Publisher:Springer
ISSN:0377-9017
Funders:Schweizerischer Nationalfonds
Additional Information:This is a post-peer-review, pre-copyedit version of an article published in Letters in Mathematical Physics. The final authenticated version is available online at: https://doi.org/10.1007/s11005-017-0959-6
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s11005-017-0959-6

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