Phase space Feynman path integrals via piecewise bicharacteristic paths and their semiclassical approximations
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Publication:924914
DOI10.1016/j.bulsci.2007.06.003zbMath1141.81018OpenAlexW2030061356MaRDI QIDQ924914
Naoto Kumano-Go, Daisuke Fujiwara
Publication date: 29 May 2008
Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.bulsci.2007.06.003
Path integrals in quantum mechanics (81S40) Applications of manifolds of mappings to the sciences (58D30) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Fourier integral operators applied to PDEs (35S30)
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Cites Work
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- 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
- Remarks on convergence of the Feynman path integrals
- A family of Fourier integral operators and the fundamental solution for a Schrödinger equation
- Mathematical theory of Feynman path integrals
- A proof of H. Kumano-go-Taniguchi theorem for multi-products of Fourier integral operators
- 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
- Remarks on pseudo-differential operators
- Quantum-mechanical path integrals with Wiener measure for all polynomial Hamiltonians. II
- STATIONARY PHASE, QUANTUM MECHANICS AND SEMI-CLASSICAL LIMIT
- 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
- An Improved Remainder Estimate of Stationary Phase Method for Some Oscillatory Integrals over a Space of Large Dimension
- Foundations for relativistic quantum theory. I. Feynman’s operator calculus and the Dyson conjectures
- Phase space Feynman path integrals
- Hamiltonian Feynman path integrals via the Chernoff formula
- Feynman Integrals and the Schrödinger Equation
- Space-Time Approach to Non-Relativistic Quantum Mechanics
- Fourier-Integral-Operator Approximation of Solutions to First-Order Hyperbolic Pseudodifferential Equations I: Convergence in Sobolev Spaces
- On the Definition and Approximation of Feynman's Path Integrals
- An Operator Calculus Having Applications in Quantum Electrodynamics
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