From Feynman-Kac formula to Feynman integrals via analytic continuation

DOI10.1016/0304-4149(94)00028-XzbMath0812.60052MaRDI QIDQ1344948

Jia'an Yan

Publication date: 14 May 1995

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

Schrödinger equationanalytic continuationFeynman-Kac formulaadditive functionalFeynman integralsBrownian bridge measuresgeneralized Kato class

Mathematics Subject Classification ID

Brownian motion (60J65) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of stochastic analysis (to PDEs, etc.) (60H30) Path integrals in quantum mechanics (81S40) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Transition functions, generators and resolvents (60J35)

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An occupation time approach for convergence of measure-valued processes, and the death process of a branching system, Imbedding of infinite dimensional distributions into simplified Colombeau type algebras, A filtration of Wick algebra and its application to quantum SDEs, A complex scaling approach to sequential Feynman integrals, Continuity of the integral kernel of Schrödinger propagator

Cites Work

• Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula
• Open quantum systems and Feynman integrals
• Mathematical theory of Feynman path integrals
• The analytic operator-valued Feynman integral via additive functionals of Brownian motion
• Schrödinger semigroups
• Space-Time Approach to Non-Relativistic Quantum Mechanics
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