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Path integrals on manifolds by finite dimensional approximation
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Christian Bär
Published/Copyright:
November 18, 2008
Abstract
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.
Received: 2007-03-16
Published Online: 2008-11-18
Published in Print: 2008-December
© Walter de Gruyter Berlin · New York 2008
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Articles in the same Issue
- On mixing and ergodicity in locally compact motion groups
- Path integrals on manifolds by finite dimensional approximation
- The Schwartz algebra of an affine Hecke algebra
- Adelic amoebas disjoint from open halfspaces
- Generalized Kac-Moody algebras, automorphic forms and Conway's group II
- A Siegel-Weil formula for automorphic characters: Cubic variation of a theme of Snitz
- Calibrated manifolds and Gauge theory
- On the gradient set of Lipschitz maps
