Heat kernel expansion: user's manual

Vassilevich, D.V.

doi:10.1016/j.physrep.2003.09.002

Cited by 1,016

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Heat kernel expansion: user's manual

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Vassilevich, D.V.·2003·Physics Reports

DOI 10.1016/j.physrep.2003.09.002

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Abstract The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients scattered in mathematical and physical literature. We present explicit expressions for these coefficients on manifolds with and without boundaries, subject to local and non-local boundary conditions, in the presence of various types of singularities (e.g., domain walls). In each case the heat kernel coefficients are given in terms of several geometric invariants. These invariants are derived for scalar and spinor theories with various interactions, Yang–Mills fields, gravity, and open bosonic strings. We discuss the relations between the heat kernel coefficients and quantum anomalies, corresponding anomalous actions, and covariant perturbation expansions of the effective action (both “low-” and “high-energy” ones).

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Authors: Vassilevich, D. V.
Venue: Physics Reports
Publisher: Elsevier BV
Published: 2003-12
Volume: 388
Issue: 5-6
Pages: 279-360
ISSN: 0370-1573 (ISSN-L)
DOI: 10.1016/j.physrep.2003.09.002
OpenAlex: W2084068075
Cited by: 1,016
References: 256
FWCI: 10.78
Type: journal article
Language: en
Open access: green
Licence: www.elsevier.com/tdm/userlicense/1.0/ (tdm)

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This page: CoChat. (2026). Citation check: Heat kernel expansion: user's manual. https://app.cochat.ai/papers/10.1016/j.physrep.2003.09.002
The paper: Vassilevich, D. V. (2003). Heat kernel expansion: user's manual. Physics Reports. https://doi.org/10.1016/j.physrep.2003.09.002

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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.

Heat kernel expansion: user's manual

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