2007/03/09 by Christian Baer, Christian Bär, Frank Pfaeffle +1
Mathematics · Physics and Astronomy · #Boundary (topology) #Geodesic #Geometric Analysis and Curvature Flows #Heat equation #Heat kernel #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Numerical methods in inverse problems #Operator (biology) #Path (computing) #Path integral formulation #Physics #Pure mathematics #Riemannian manifold #Space (punctuation) #TRACE (psycholinguistics) #advanced mathematical theories #math-ph #math.AP #math.DG #math.MP #math.PR #msc:47D06 #msc:58J35 #msc:58J65
paper · pdf · doi:10.1515/crelle.2008.089
published as Journal für die reine und angewandte Mathematik (Crelles Journal) 625, 29-57 (2008) · 23 pages
arxiv created 2007/03/09 · openalex publication_date 2008/01/01 · arxiv updated 2012/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let M be a compact Riemannian manifold without boundary and let H be a self-adjoint generalized Laplace operator acting on sections in a bundle over M . We give a path integral formula for the solution to the corresponding heat equation. This is based on approximating path space by finite dimensional spaces of geodesic polygons. We also show a uniform convergence result for the heat kernels. This yields a simple and natural proof for the Hess-Schrader-Uhlenbrock estimate and a path integral formula for the trace of the heat operator.