Heat kernel: proper time method, Fock-Schwinger gauge, path integral representation, and Wilson line

• Main Authors: Ivanov, A. V, Kharuk, N. V
• Format: Journal Article
• Language: English
• Published: 27-01-2020
• Subjects: Mathematics - Mathematical Physics; Physics - High Energy Physics - Theory; Physics - Mathematical Physics
• DOI: 10.48550/arxiv.1906.04019

Theor Math Phys 205, 1456--1472 (2020) The proper time method plays an important role in modern mathematics and
physics. It includes many approaches, each of which has its pros and cons. This
work is devoted to the description of one model case, which reflects the
subtleties of construction and can be extended to a more general cases (curved
space, manifold with boundary), and contains two interrelated parts: asymptotic
expansion and path intergal representation. The paper discusses in details the
importance of gauge conditions and role of the ordered exponentials, gives the
proof of a new non-recursive formula for the Seeley-DeWitt coefficients on the
diagonal, as well as the equivalence of the two main approaches using the
exponential formula.