Smooth functional derivatives in Feynman path integrals by time slicing approximation

DOI10.1016/j.bulsci.2004.09.003zbMath1070.81083OpenAlexW2160673941MaRDI QIDQ2484957

Daisuke Fujiwara, Naoto Kumano-Go

Publication date: 3 August 2005

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

Full work available at URL: https://doi.org/10.1016/j.bulsci.2004.09.003

zbMATH Keywords

Stochastic analysisFourier integral operatorsPath integrals

Mathematics Subject Classification ID

Path integrals in quantum mechanics (81S40) Applications of manifolds of mappings to the sciences (58D30) Stochastic calculus of variations and the Malliavin calculus (60H07) Fourier integral operators applied to PDEs (35S30)

Related Items (14)

Convergence in \(L^{p}\) for Feynman path integrals ⋮ The time-dependent quartic oscillator --- a Feynman path integral approach ⋮ 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 ⋮ 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 ⋮ The second term of the semi-classical asymptotic expansion for Feynman path integrals with integrand of polynomial growth ⋮ Approximation of Feynman path integrals with non-smooth potentials ⋮ Feynman path integrals for the inverse quartic oscillator ⋮ Phase space Feynman path integrals of higher order parabolic type with general functional as integrand

Cites Work

• Feynman path integrals as analysis on path space by time slicing approximation
• 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
• Space-Time Approach to Non-Relativistic Quantum Mechanics
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