Path integrals on manifolds by finite dimensional approximation

DOI10.1515/CRELLE.2008.089zbMath1165.58015arXivmath/0703272MaRDI QIDQ3600016

Frank Pfäffle, Christian Bär

Publication date: 10 February 2009

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703272

zbMATH Keywords

path integralRiemannian manifoldfinite dimensional approximationHess-Schrader-Uhlenbrock estimate

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (7)

Approximation schemes for path integration on Riemannian manifolds ⋮ Path integrals on manifolds with boundary ⋮ Chernoff approximations of Feller semigroups in Riemannian manifolds ⋮ Path integrals, supersymmetric quantum mechanics, and the Atiyah-Singer index theorem for twisted Dirac ⋮ An approximation to Wiener measure and quantization of the Hamiltonian on manifolds with non-positive sectional curvature ⋮ A rigorous path integral for supersymmetic quantum mechanics and the heat kernel ⋮ The Chern-Gauss-Bonnet theorem via supersymmetric Euclidean field theories

Cites Work

• Positive scalar curvature and the Dirac operator on complete Riemannian manifolds
• Chernoff's theorem and discrete time approximations of Brownian motion on manifolds
• Heat operator and \(\zeta\)-function estimates for surfaces
• Finite dimensional approximations to Wiener measure and path integral formulas on manifolds
• Note on product formulas for operator semigroups
• Heat equation derivative formulas for vector bundles

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