Path integrals as analysis on path space by time slicing approximation

DOI10.1090/suga/469zbMath1522.81170OpenAlexW4290770306WikidataQ114093803 ScholiaQ114093803MaRDI QIDQ6095856

Naoto Kumano-Go

Publication date: 8 September 2023

Published in: Sugaku Expositions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/suga/469

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Path integrals in quantum mechanics (81S40) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Fourier integral operators applied to PDEs (35S30)

Cites Work

• An integration by parts formula for Feynman path integrals
• Phase space Feynman path integrals with smooth functional derivatives by time slicing approximation
• Feynman path integrals as analysis on path space by time slicing approximation
• A mathematical theory of the phase space Feynman path integral of the functional
• Phase space Feynman path integrals via piecewise bicharacteristic paths and their semiclassical approximations
• Generalized Brownian functionals and the Feynman integral
• Remarks on convergence of the Feynman path integrals
• A family of Fourier integral operators and the fundamental solution for a Schrödinger equation
• Schrödinger evolution equations with magnetic fields
• On the formulation of the Feynman path integral through broken line paths
• The time slicing approximation of the fundamental solution for the Schrödinger equation with electromagnetic fields
• Phase space Feynman path integrals of parabolic type with smooth functional derivatives
• Phase space Feynman path integrals of higher order parabolic type with general functional as integrand
• Mathematical theory of Feynman path integrals. An introduction
• Smooth functional derivatives in Feynman path integrals by time slicing approximation
• The second term of the semi-classical asymptotic expansion for Feynman path integrals with integrand of polynomial growth
• Feynman's path integral. Definition without limiting procedure
• Quantum-mechanical path integrals with Wiener measure for all polynomial Hamiltonians. II
• A Family of Integrals Serving to Connect the Wiener and Feynman Integrals
• A simple definition of the Feynman integral, with applications
• The stationary phase method with an estimate of the remainder term on a space of large dimension
• A Modern Approach to Functional Integration
• Feynman Integrals and the Schrödinger Equation
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• Hamiltonian Path-Integral Methods
• An Operator Calculus Having Applications in Quantum Electrodynamics
• Functional Integration
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Path integrals as analysis on path space by time slicing approximation