https://doi.org/10.1140/epjp/s13360-022-03176-7
Regular Article
Special functions for heat kernel expansion
1
St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, 27 Fontanka, 191023, Saint Petersburg, Russia
2
Leonhard Euler International Mathematical Institute, 10 Pesochnaya nab, 197022, Saint Petersburg, Russia
3
ITMO University, 197101, Saint Petersburg, Russia
Received:
1
May
2022
Accepted:
9
August
2022
Published online:
17
September
2022
In this paper, we study an asymptotic expansion of the heat kernel for a Laplace operator on a smooth Riemannian manifold without a boundary at enough small values of the proper time. The Seeley–DeWitt coefficients of this decomposition satisfy a set of recurrence relations, which we use to construct two function families of a special kind. Using these functions, we study the expansion of a local heat kernel for the inverse Laplace operator. We show that the new functions have some important properties. For example, we can consider the Laplace operator on the function set as a shift one. Also, we describe various applications useful in theoretical physics and, in particular, we find a decomposition of local Green’s functions near the diagonal in terms of new functions.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
