Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-12-17
Lect.Notes Phys.807:193-259,2010
Physics
High Energy Physics
High Energy Physics - Theory
71 pages, 2 figures, submitted for publication in the Springer book (in preparation) "Quantum Gravity", edited by B. Booss-Bav
Scientific paper
10.1007/978-3-642-11897-5_4
We review the status of covariant methods in quantum field theory and quantum gravity, in particular, some recent progress in the calculation of the effective action via the heat kernel method. We study the heat kernel associated with an elliptic second-order partial differential operator of Laplace type acting on smooth sections of a vector bundle over a Riemannian manifold without boundary. We develop a manifestly covariant method for computation of the heat kernel asymptotic expansion as well as new algebraic methods for calculation of the heat kernel for covariantly constant background, in particular, on homogeneous bundles over symmetric spaces, which enables one to compute the low-energy non-perturbative effective action.
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