2006/06/30 by L. L. Salcedo, L.L. Salcedo · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Connection (principal bundle) #Covariant derivative #Covariant transformation #Diagonal #Gauge covariant derivative #Matrix (chemical analysis) #Noncommutative and Quantum Gravity Theories #Operator (biology) #Spectral Theory in Mathematical Physics #gr-qc #hep-th
paper · pdf · doi:10.1140/epjc/s10052-006-0133-2
published as Eur.Phys.J.C49:831-850,2007 · 28 pages, no figures. References added. To appear in European Physical Journal C
arxiv created 2006/09/11 · openalex publication_date 2006/11/24 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.