A REPRESENTATION OF THE BELAVKIN EQUATION VIA PHASE SPACE FEYNMAN PATH INTEGRALS

DOI10.1142/S0219025704001748zbMath1077.81063OpenAlexW2085956751WikidataQ62049364 ScholiaQ62049364MaRDI QIDQ4652883

Giuseppina Guatteri, Sonia Mazzucchi, Sergio A. Albeverio

Publication date: 28 February 2005

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219025704001748

zbMATH Keywords

quantum theoryphase spacestochastic PDEsoscillatory integralsFeynman path integralsstochastic characteristicscontinuous measurementBelavkin equation

Mathematics Subject Classification ID

Path integrals in quantum mechanics (81S40) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

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Generalized Scaling Operators in White Noise Analysis and Applications to Hamiltonian Path Integrals with Quadratic Action ⋮ The time-dependent quartic oscillator --- a Feynman path integral approach ⋮ Effective approximation for a nonlocal stochastic Schrödinger equation with oscillating potential ⋮ A rigorous approach to the Feynman-Vernon influence functional and its applications. I ⋮ Mathematical theory of Feynman path integrals ⋮ Generalized Feynman path integrals and applications to higher-order heat-type equations ⋮ A unified approach to infinite-dimensional integration ⋮ DISCONTINUITY OF FOURIER TRANSFORMS OF POISSONIAN TYPE COUNTABLY ADDITIVE MEASURES

Cites Work

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• Semigroups of linear operators and applications to partial differential equations
• Mathematical theory of Feynman path integrals
• Finite dimensional approximation approach to oscillatory integrals and stationary phase in infinite dimensions
• Continuous quantum jumps and infinite-dimensional stochastic equations
• Continuous Quantum Measurement: Local and Global Approaches
• Phase space Feynman path integrals
• Asymptotic behavior of infinite dimensional stochastic differential equations by anticipative variation of constants formula

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