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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 205, Number 2, Pages 242–261
DOI: https://doi.org/10.4213/tmf9923 (Mi tmf9923) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Heat kernel: Proper-time method, Fock–Schwinger gauge, path integral, and Wilson line

A. V. Ivanova, N. V. Kharukb

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg National Research University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia
Full-text PDF (593 kB) Citations (12)
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DOI: https://doi.org/10.4213/tmf9923
Abstract: This paper is devoted to the proper-time method and describes a model case that reflects the subtleties of constructing the heat kernel, is easily extended to more general cases (curved space, manifold with a boundary), and contains two interrelated parts: an asymptotic expansion and a path integral representation. We discuss the significance of gauge conditions and the role of ordered exponentials in detail, derive a new nonrecursive formula for the Seeley–DeWitt coefficients on the diagonal, and show the equivalence of two main approaches using the exponential formula.
Keywords: path integral, Wilson line, ordered exponential, Fock–Schwinger gauge, Laplace operator, heat kernel, Seeley–DeWitt coefficient, proper time method.
Funding agency Grant number
Russian Science Foundation 18-11-00297
Contest «Young Russian Mathematics»
This research was supported by a grant from the Russian Science Foundation (Project No. 18-11-00297). A. V. Ivanov is a winner of the Young Russian Mathematician award and thanks its sponsors and jury.
Received: 20.04.2020
Revised: 20.04.2020
English version:
Theoretical and Mathematical Physics, 2020, Volume 205, Issue 2, Pages 1456–1472
DOI: https://doi.org/10.1134/S0040577920110057
Bibliographic databases:
Document Type: Article
PACS: 11.10.Jj
MSC: 35K08
Language: Russian
Citation: A. V. Ivanov, N. V. Kharuk, “Heat kernel: Proper-time method, Fock–Schwinger gauge, path integral, and Wilson line”, TMF, 205:2 (2020), 242–261; Theoret. and Math. Phys., 205:2 (2020), 1456–1472
Citation in format AMSBIB
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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