New Algebraic Methods for Calculating the Heat Kernel and Effective Action in Quantum Gravity and Gauge Theories

Abstract

An overview about recent progress in the calculation of the heat kernel and the one-loop effective action in quantum gravity and gauge theories is given. We analyse the general structure of the standard Schwinger-De Witt asymptotic expansion and discuss the applicability of that to the case of strongly curved manifolds and strong background fields. We argue that the low-energy limit in gauge theories and quantum gravity, when formulated in a covariant way, should be related to background fields with covariantly constant curvature, gauge field strength and potential term. It is shown that the condition of the covariant constancy of the background curvatures brings into existence some Lie algebra. The heat kernel operator for the Laplace operator is presented then as an average over the corresponding Lie group with some nontrivial Gaussian measure. Using this representation the heat kernel diagonal is obtained. The result is expressed purely in terms of curvature invariants and is explicitly covariant. Related topics concerning the structure of symmetric spaces and the calculation of the effective action are discussed.

22 pages, Plain TeX, University of Greifswald (August, 1994)

References in corpus (4)

• Covariant methods for the calculation of the effective action in quantum field theory and investigation of higher-derivative quantum gravity
• The heat kernel on symmetric spaces via integrating over the group of isometries
• One-loop effective potential on hyperbolic manifolds
• Self-interacting scalar fields on spacetime with compact hyperbolic spatial part

Cited by in corpus (4)

• On Higher Order Gravities, Their Analogy to GR, and Dimensional Dependent Version of Duff's Trace Anomaly Relation
• A model of stable chromomagnetic vacuum in higher-dimensional Yang-Mills theory
• Nonperturbative methods for calculating the heat kernel
• Heat Kernel Asymptotics on Symmetric Spaces