Feynman path integrals as infinite-dimensional oscillatory integrals: Some new developments

DOI10.1007/BF00994909zbMath0813.58009MaRDI QIDQ1332516

Zdzisław Brzeźniak, Sergio A. Albeverio

Publication date: 14 May 1995

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

zbMATH Keywords

trace formulaoscillatory integralsFeynman path integral

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Asymptotic expansions of solutions to PDEs (35C20) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Applications of manifolds of mappings to the sciences (58D30) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Applications of functional analysis in quantum physics (46N50) Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25) Fourier integral operators applied to PDEs (35S30)

Related Items

Feynman path integrals on phase space and the metaplectic representation ⋮ The mean value for infinite volume measures, infinite products, and heuristic infinite dimensional Lebesgue measures ⋮ Oscillatory integrals on Hilbert spaces and Schrödinger equation with magnetic fields ⋮ Mathematical theory of Feynman path integrals ⋮ The Trace Formula for Schrödinger Operators from Infinite Dimensional Oscillatory Integrals

Cites Work

• The method of stationary phase for oscillatory integrals on Hilbert spaces
• Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula
• Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics. I
• Feynman path integrals and the trace formula for the Schrödinger operators
• Chaos in classical and quantum mechanics
• Gaussian measures in Banach spaces
• Mathematical theory of Feynman path integrals
• Product formulas for the eigenvalues of a class of boundary value problems
• On the eigenvalues of a disturbed harmonic oscillator
• Formule de Poisson pour les variétés riemanniennes
• Finite dimensional approximation approach to oscillatory integrals and stationary phase in infinite dimensions
• The Ilstow and Feynman integrals
• Some remarks on the Feynman–Kac formula
• Spectre D'Un hamiltonien quantique et mecanique classique
• Classical mechanics, the diffusion (heat) equation, and the Schrödinger equation
• Oscillatory integrals on Hilbert spaces and Schrödinger equation with magnetic fields
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item