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Mathematical Physics

arXiv:1807.11782 (math-ph)
[Submitted on 31 Jul 2018 (v1), last revised 11 Oct 2019 (this version, v3)]

Title:Globalization for Perturbative Quantization of Nonlinear Split AKSZ Sigma Models on Manifolds with Boundary

Authors:Alberto S. Cattaneo, Nima Moshayedi, Konstantin Wernli
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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.
Comments: 41 pages, 9 figures, typos fixed, presentation improved for non experts, to appear in Commun. Math. Phys
Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA); Symplectic Geometry (math.SG)
Cite as: arXiv:1807.11782 [math-ph]
  (or arXiv:1807.11782v3 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1807.11782
Journal reference: Commun. Math. Phys. 372.1 pp 213-260 (2019)
Related DOI: https://doi.org/10.1007/s00220-019-03591-5

Submission history

From: Nima Moshayedi [view email]
[v1] Tue, 31 Jul 2018 12:10:02 UTC (49 KB)
[v2] Tue, 11 Jun 2019 14:34:29 UTC (78 KB)
[v3] Fri, 11 Oct 2019 08:41:39 UTC (78 KB)
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