The analytic operator-valued Feynman integral via additive functionals of Brownian motion

DOI10.1007/BF01064169zbMath0843.28006OpenAlexW2027463060MaRDI QIDQ1909378

Gerald W. Johnson, Zhi-Ming Ma, Sergio A. Albeverio

Publication date: 1 May 1996

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

Full work available at URL: https://doi.org/10.1007/bf01064169

zbMATH Keywords

perturbationsMarkov processesDirichlet formFeynman-Kac formulaFeynman path integralanalytic operator-valued Feynman integral

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Path integrals in quantum mechanics (81S40) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items (5)

From Feynman-Kac formula to Feynman integrals via analytic continuation ⋮ Semilinear elliptic equations with Dirichlet operator and singular nonlinearities ⋮ A dominated-type convergence theorem for the Feynman integral ⋮ Stability theorem for the Feynman integral via time continuation ⋮ A remark on the heat equation with a point perturbation, the Feynman-Kac formula with local time and derivative pricing

Cites Work

• The method of stationary phase for oscillatory integrals on Hilbert spaces
• Product formula for imaginary resolvents with application to a modified Feynman integral
• Perturbation of Dirichlet forms --- lower semiboundedness, closability, and form cores
• Finite dimensional approximation approach to oscillatory integrals and stationary phase in infinite dimensions
• Schrödinger semigroups
• A Family of Integrals Serving to Connect the Wiener and Feynman Integrals
• Space-Time Approach to Non-Relativistic Quantum Mechanics
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