Feynman path integrals as analysis on path space by time slicing approximation

DOI10.1016/j.bulsci.2004.01.002zbMath1059.81110OpenAlexW1988781546MaRDI QIDQ707262

Naoto Kumano-Go

Publication date: 9 February 2005

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2004.01.002

zbMATH Keywords

path integralsconvergence of path integralstime slicing

Mathematics Subject Classification ID

Integrals of Riemann, Stieltjes and Lebesgue type (26A42) Path integrals in quantum mechanics (81S40) Stochastic calculus of variations and the Malliavin calculus (60H07) Fourier integral operators applied to PDEs (35S30)

Related Items

Convergence in \(L^{p}\) for Feynman path integrals, Probability and Quantum Symmetries. II. The Theorem of Nœther in quantum mechanics, The time-dependent quartic oscillator --- a Feynman path integral approach, A mathematical theory of the phase space Feynman path integral of the functional, Fourier-integral-operator product representation of solutions to first-order symmetrizable hyperbolic systems, An integration by parts formula for Feynman path integrals, On the pointwise convergence of the integral kernels in the Feynman-Trotter formula, Path integrals as analysis on path space by time slicing approximation, Fluctuations and temperature effects in bose-einstein condensation, Phase space Feynman path integrals via piecewise bicharacteristic paths and their semiclassical approximations, Phase space Feynman path integrals with smooth functional derivatives by time slicing approximation, Mathematical theory of Feynman path integrals, On the time slicing approximation of Feynman path integrals for non-smooth potentials, 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, Timeless configuration space and the emergence of classical behavior, Approximation of Feynman path integrals with non-smooth potentials, Time-slicing approximation of Feynman path integrals on compact manifolds

Cites Work

• 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
• Mathematical theory of Feynman path integrals
• A proof of H. Kumano-go-Taniguchi theorem for multi-products of Fourier integral operators
• 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
• Remarks on pseudo-differential operators
• A Family of Integrals Serving to Connect the Wiener and Feynman Integrals
• The stationary phase method with an estimate of the remainder term on a space of large dimension
• Feynman Integrals and the Schrödinger Equation
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• A New Representation for Stochastic Integrals and Equations
• Stochastic integral
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item