Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-02-29
in: Global Analysis, Differential Geometry and Lie Algebras, Ed. G. Tsagas, (Bucharest: Geometry Balkan Press, 1998), pp. 7-21
Physics
High Energy Physics
High Energy Physics - Theory
15 pages, Plain TeX, 42 KB, no figures; Talk given at the Int. Conf. `Global Analysis, Differential Geometry and Lie Algebras'
Scientific paper
We study the low-energy approximation for calculation of the heat kernel which is determined by the strong slowly varying background fields in strongly curved quasi-homogeneous manifolds. A new covariant algebraic approach, based on taking into account a finite number of low-order covariant derivatives of the background fields and neglecting all covariant derivatives of higher orders, is proposed. It is shown that a set of covariant differential operators together with the background fields and their low-order derivatives generates a finite dimensional Lie algebra. This algebraic structure can be used to present the heat semigroup operator in the form of an average over the corresponding Lie group. Closed covariant formulas for the heat kernel diagonal are obtained. These formulas serve, in particular, as the generating functions for the whole sequence of the Hadamard-\-Minakshisundaram-\-De~Witt-\-Seeley coefficients in all symmetric spaces.
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