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Globalization for perturbative quantization of nonlinear split AKSZ Sigma Models on manifolds with boundary


Cattaneo, Alberto Sergio; Moshayedi, Nima; Wernli, Konstantin Walter (2019). Globalization for perturbative quantization of nonlinear split AKSZ Sigma Models on manifolds with boundary. Communications in Mathematical Physics, 372(1):213-260.

Abstract

We describe a covariant framework to construct a globalized version for the perturbative quantization of nonlinear split AKSZ Sigma Models on manifolds with and without boundary, and show that it captures the change of the quantum state as one changes the constant map around which one perturbs. This is done by using concepts of formal geometry. Moreover, we show that the globalized quantum state can be interpreted as a closed section with respect to an operator that squares to zero. This condition is a generalization of the modified Quantum Master Equation as in the BV-BFV formalism, which we call the modified “differential” Quantum Master Equation.

Abstract

We describe a covariant framework to construct a globalized version for the perturbative quantization of nonlinear split AKSZ Sigma Models on manifolds with and without boundary, and show that it captures the change of the quantum state as one changes the constant map around which one perturbs. This is done by using concepts of formal geometry. Moreover, we show that the globalized quantum state can be interpreted as a closed section with respect to an operator that squares to zero. This condition is a generalization of the modified Quantum Master Equation as in the BV-BFV formalism, which we call the modified “differential” Quantum Master Equation.

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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
Scopus Subject Areas:Physical Sciences > Statistical and Nonlinear Physics
Physical Sciences > Mathematical Physics
Uncontrolled Keywords:Mathematical Physics, Statistical and Nonlinear Physics
Language:English
Date:8 November 2019
Deposited On:16 Dec 2019 07:24
Last Modified:29 Jul 2020 11:49
Publisher:Springer
ISSN:0010-3616
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/s00220-019-03591-5

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