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

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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 15 scientific papers (total in 15 papers)

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

A. V. Ivanov^a, N. V. Kharuk^b

^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 (15)

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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

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Linking options:

https://www.mathnet.ru/eng/tmf9923

https://doi.org/10.4213/tmf9923

https://www.mathnet.ru/eng/tmf/v205/i2/p242

This publication is cited in the following 15 articles:

A. V. Ivanov, N. V. Kharuk, “Three-Loop Divergences in Effective Action of 4-Dimensional Yang–Mills Theory with Cutoff Regularization: ${\Gamma }_{4}^{2}$ -Contribution”, J Math Sci, 2024
Upalaparna Banerjee, Joydeep Chakrabortty, Kaanapuli Ramkumar, “Renormalization of scalar and fermion interacting field theory for arbitrary loop: Heat–Kernel approach”, Eur. Phys. J. Plus, 139:8 (2024)
A. V. Ivanov, “Lokalnoe teplovoe yadro”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 30, Zap. nauchn. sem. POMI, 532, POMI, SPb., 2024, 136–152
A. V. Ivanov, N. V. Kharuk, “Trekhpetlevye raskhodimosti v effektivnom deistvii $4$ -kh mernoi teorii Yanga–Millsa s regulyarizatsiei obrezaniem: $\Gamma_4^2$ -vklad”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 29, Zap. nauchn. sem. POMI, 520, POMI, SPb., 2023, 162–188
A. V. Ivanov, N. V. Kharuk, “Ordered exponential and its features in Yang–Mills effective action”, Commun. Theor. Phys., 75:8 (2023), 085202
P. V. Akacevich, A. V. Ivanov, “On two-loop effective action of 2d sigma model”, Eur. Phys. J. C, 83:7 (2023), 653
N. V. Kharuk, “Zero Modes of the Laplace Operator in Two-Loop Calculations in the Yang-Mills Theory”, J Math Sci, 275:3 (2023), 370
A. V. Ivanov, N. V. Kharuk, “Formula for two-loop divergent part of 4-D Yang–Mills effective action”, Eur. Phys. J. C, 82:11 (2022)
A. V. Ivanov, N. V. Kharuk, “Special functions for heat kernel expansion”, Eur. Phys. J. Plus, 137:9 (2022)
A. O. Barvinsky, W. Wachowski, “Heat kernel expansion for higher order minimal and nonminimal operators”, Phys. Rev. D, 105:6 (2022)
N. V. Kharuk, “Nulevye mody operatora Laplasa v dvukhpetlevykh vychisleniyakh v teorii Yanga–Millsa”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 28, Zap. nauchn. sem. POMI, 509, POMI, SPb., 2021, 216–226
A. V. Ivanov, “Notes on Functional Integration”, J Math Sci, 257:4 (2021), 518
A. V. Ivanov, N. V. Kharuk, “Quantum Equation of Motion and Two-Loop Cutoff Renormalization for 𝜙3 Model”, J Math Sci, 257:4 (2021), 526
A V Ivanov, N V Kharuk, “Two-loop cutoff renormalization of 4-D Yang–Mills effective action”, J. Phys. G: Nucl. Part. Phys., 48:1 (2020), 015002
N. V. Kharuk, “Mixed type regularizations and nonlogarithmic singularities”, J Math Sci, 264:3 (2022), 362

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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