The heat kernel on symmetric spaces via integrating over the group of isometries

1994/09/01 by Ivan G. Avramidi · 28 citations
Chemistry · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Algebraic number #Chemistry #Constant curvature #Curvature #Diagonal #Geometric Analysis and Curvature Flows #Geometry #Group (periodic table) #Heat kernel #Isotropy #Kernel (algebra) #Laplace operator #Laplace transform #Lie group #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Operator (biology) #Physics #Pure mathematics #advanced mathematical theories #hep-th

paper · pdf · doi:10.1016/0370-2693(94)00994-5

published in Physics Letters B 336(2), 171-177 (Elsevier BV) · 8 pages, Plain TeX, 21 KB, no figures

openalex publication_date 1994/09/01 · arxiv created 1995/09/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A new algebraic approach for calculating the heat kernel for the Laplace operator on any Riemannian manifold with covariantly constant curvature is proposed. It is shown that the heat kernel operator can be obtained by an averaging over the Lie group of isometries. The heat kernel diagonal is obtained in form of an integral over the isotropy subgroup.

Citations

• Quantum field theories on manifolds with curved boundaries: Scalar fields
• Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds

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• HEAT KERNEL ON HOMOGENEOUS BUNDLES
• Eternity and the cosmological constant