Classical mechanics, the diffusion (heat) equation and the Schrödinger equation on a Riemannian manifold

DOI10.1063/1.524784zbMath0485.70024OpenAlexW1986767695WikidataQ115332634 ScholiaQ115332634MaRDI QIDQ3945655

Aubrey Truman

Publication date: 1981

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.524784

zbMATH Keywords

Wiener processpath integralsLaplace-Beltrami operatorFeynman-Kac formulaCameron-Martin- Grisanov type formulaorthogonal frame bundleperturbed heat and Schrödinger equations on Riemann manifoldquasi-classical limits

Mathematics Subject Classification ID

Path integrals in quantum mechanics (81S40) Applications of manifolds of mappings to the sciences (58D30) Stochastic mechanics (including stochastic electrodynamics) (81P20) Lagrange's equations (70H03) General models, approaches, and methods in mechanics of particles and systems (70G99)

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Cites Work

• Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics. I
• A class of approximations of Brownian motion
• A generalized Sturm theorem
• A special Stoke's theorem for complete Riemannian manifolds
• DIFFUSION PROCESSES AND RIEMANNIAN GEOMETRY
• Classical mechanics, the diffusion (heat) equation, and the Schrödinger equation
• Oscillatory integrals, lagrange immersions and unfolding of singularities
• Dynamical Theory in Curved Spaces. I. A Review of the Classical and Quantum Action Principles