scientific article

zbMath0446.60045MaRDI QIDQ3891511

Barry L. Nelson, G. S. Sammelman, K. David Elworthy, Cecile de Witt-Morette

Publication date: 1980

Full work available at URL: http://www.numdam.org/item?id=AIHPA_1980__32_4_327_0

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

external gauge fieldcurved spacehistorical discussionFeynman path integrationmultiply connected configuration space

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Diffusion processes (60J60) Path integrals in quantum mechanics (81S40) Applications of manifolds of mappings to the sciences (58D30) Diffusion processes and stochastic analysis on manifolds (58J65) Stochastic integrals (60H05) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory (81-01)

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Path integrals with discarded degrees of freedom, Quantum effective potential from discarded degrees of freedom, Path integration over closed loops and Gutzwiller's trace formula, Quantum confinement for the curvature Laplacian \(- \Delta + cK\) on 2D-almost-Riemannian manifolds, The surface limit of Brownian motion in tubular neighborhoods of an embedded Riemannian manifold., Path integration for velocity-dependent potentials, Finite dimensional approximations to Wiener measure and path integral formulas on manifolds, Transformations of measures via their generalized densities

Cites Work

• On the heat kernel of a complete Riemannian manifold
• Path integration for velocity-dependent potentials
• Conservation of Isotopic Spin and Isotopic Gauge Invariance
• Classical mechanics, the diffusion (heat) equation and the Schrödinger equation on a Riemannian manifold
• Classical mechanics, the diffusion (heat) equation, and the Schrödinger equation
• Dynamical Theory in Curved Spaces. I. A Review of the Classical and Quantum Action Principles
• On the Definition and Approximation of Feynman's Path Integrals
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