ON CONVERGENCE OF THE FEYNMAN PATH INTEGRAL FORMULATED THROUGH BROKEN LINE PATHS

DOI10.1142/S0129055X99000313zbMath0969.81034MaRDI QIDQ4519817

Wataru Ichinose

Publication date: 4 December 2000

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

zbMATH Keywords

weighted Sobolev spacesgauge invariantproof of convergenceprobability amplitudenonrelativisticboundedness theorem

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Path integrals in quantum mechanics (81S40) Applications of manifolds of mappings to the sciences (58D30)

Related Items (9)

Notes on the Feynman path integral for the Dirac equation ⋮ A mathematical theory of the phase space Feynman path integral of the functional ⋮ Notes on the Cauchy problem for the self-adjoint and non-self-adjoint Schrödinger equations with polynomially growing potentials ⋮ On the Feynman path integral for the magnetic Schrödinger equation with a polynomially growing electromagnetic potential ⋮ On the mathematical formulation of the restricted Feynman path integrals through broken line paths ⋮ An approximation to Wiener measure and quantization of the Hamiltonian on manifolds with non-positive sectional curvature ⋮ THE PHASE SPACE FEYNMAN PATH INTEGRAL WITH GAUGE INVARIANCE AND ITS CONVERGENCE ⋮ On the Feynman path integral for the Dirac equation in the general dimensional spacetime ⋮ ON THE FEYNMAN PATH INTEGRAL FOR NONRELATIVISTIC QUANTUM ELECTRODYNAMICS

Cites Work

• Jump-type processes and their applications in quantum mechanics
• Remarks on convergence of the Feynman path integrals
• On the formulation of the Feynman path integral through broken line paths
• Oscillatory integrals on Hilbert spaces and Schrödinger equation with magnetic fields
• Space-Time Approach to Non-Relativistic Quantum Mechanics

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