2008/12/17 by Ivan G. Avramidi, I.G. Avramidi
Mathematics · Physics and Astronomy · #Action (physics) #Advanced Operator Algebra Research #Covariant transformation #Effective action #Geometric Analysis and Curvature Flows #Heat kernel #Heat kernel signature #Kernel (algebra) #Quantum field theory #Quantum gravity #Spectral Theory in Mathematical Physics #hep-th
paper · pdf · doi:10.1007/978-3-642-11897-5_4
published as Lect.Notes Phys.807:193-259,2010 · 71 pages, 2 figures, submitted for publication in the Springer book (in preparation) "Quantum Gravity", edited by B. Booss-Bavnbek, G. Esposito and M. Lesch
arxiv created 2008/12/17 · openalex publication_date 2010/01/01 · arxiv updated 2014/06/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.