This article is cited in 15 papers

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

A. V. Ivanov^a, N. V. Kharuk<sup>b

a</sup> 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

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.

PACS: 11.10.Jj

MSC: 35K08

Received: 20.04.2020
Revised: 20.04.2020

DOI: 10.4213/tmf9923

 English version: Theoretical and Mathematical Physics, 2020, 205:2, 1456–1472

Bibliographic databases:

• 
• 
• 
• 
•