Special Functions for Heat Kernel Expansion

Abstract

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 Green's functions near the diagonal in terms of new functions.

LaTeX, 22 pages, 3 figures; The second version contains more detailed description

References in corpus (5)

• Heat kernel expansion for higher order minimal and nonminimal operators
• Diagram technique for the heat kernel of the covariant Laplace operator
• Formula for two-loop divergent part of 4-D Yang-Mills effective action
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• On Two-Loop Effective Action of 2D Sigma Model
• Effective actions, cutoff regularization, quasi-locality, and gluing of partition functions
• Ordered Exponential and Its Features in Yang-Mills Effective Action
• Three-loop renormalization of the quantum action for a five-dimensional scalar cubic model with the usage of the background field method and a cutoff regularization
• Functorial properties of Schwinger-DeWitt expansion and Mellin-Barnes representation