Geodesic
Heat kernel: Proper-time method, Fock--Schwinger gauge, path integral, and Wilson line
Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 2, pp. 242-261

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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. 
@article{TMF_2020_205_2_a4,
     author = {A. V. Ivanov and N. V. Kharuk},
     title = {Heat kernel: {Proper-time} method, {Fock--Schwinger} gauge, path integral, and {Wilson} line},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {242--261},
     publisher = {mathdoc},
     volume = {205},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_205_2_a4/}
}
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A. V. Ivanov; N. V. Kharuk. Heat kernel: Proper-time method, Fock--Schwinger gauge, path integral, and Wilson line. Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 2, pp. 242-261. http://geodesic.mathdoc.fr/item/TMF_2020_205_2_a4/