The method of covariant symbols in curved space-time

Details The method of covariant symbols in curved space-time The method of covariant symbols in curved space-time

2006-06-08

arxiv.org/abs/hep-th/0606071v2

Eur.Phys.J.C49:831-850,2007

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, no figures. References added. To appear in European Physical Journal C

Scientific paper

10.1140/epjc/s10052-006-0133-2

Diagonal matrix elements of pseudodifferential operators are needed in order to compute effective Lagrangians and currents. For this purpose the method of symbols is often used, which however lacks manifest covariance. In this work the method of covariant symbols, introduced by Pletnev and Banin, is extended to curved space-time with arbitrary gauge and coordinate connections. For the Riemannian connection we compute the covariant symbols corresponding to external fields, the covariant derivative and the Laplacian, to fourth order in a covariant derivative expansion. This allows to obtain the covariant symbol of general operators to the same order. The procedure is illustrated by computing the diagonal matrix element of a nontrivial operator to second order. Applications of the method are discussed.

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