New algorithm for asymptotic expansions of the heat kernel

Details New algorithm for asymptotic expansions of the heat kernel New algorithm for asymptotic expansions of the heat kernel

Apr 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987phrvd..35.2440l&link_type=abstract

Physical Review D (Particles and Fields), Volume 35, Issue 8, 15 April 1987, pp.2440-2447

Physics

7

Asymptotic Problems And Properties

Scientific paper

A new algorithm generating asymptotic expansions for general minimal differential operators of any order is derived. At each space-time point we introduce a tangent space forming the normal-coordinate system and a fiber frame obtained by a parallel transportation from the base point. The differential operators can be reexpressed in this local representation of vector bundle. With these operators we consider the heat kernels and derive an algorithm for the asymptotic expansions. We apply this method to most general fourth-order minimal differential operators in a curved space-time and find the first two terms of the expansions including the divergencelike terms which had been neglected in many calculations. Some interesting cases of general higher-order operators are also considered.

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