Integral kernel operators on Fock space. -- Generalizations and applications to quantum dynamics

DOI10.1023/A:1005777929658zbMath0901.46033OpenAlexW10988039MaRDI QIDQ1355854

Nobuaki Obata

Publication date: 28 May 1997

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

Full work available at URL: https://doi.org/10.1023/a:1005777929658

zbMATH Keywords

white noise calculusquantum Langevin equationLie algebra of vector fieldsquantum stochastic integralsGaussian spaceFubini type theoremquantum stochastic integraliterated integrationpartial integrationintegral kernel operatoroperator-valued distributionoperators on boson Fock spaceparticle flux densitypointwise derivatives of annihilation and creation operatorsquantum Hitsuda-Skorokhod integralwhite noise distribution

Mathematics Subject Classification ID

Quantum stochastic calculus (81S25) Stochastic integrals (60H05) Linear operators on function spaces (general) (47B38) Measures and integration on abstract linear spaces (46G12) Spaces of linear operators; topological tensor products; approximation properties (46A32) Distributions on infinite-dimensional spaces (46F25)

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Evolution systems and continuity equations for white noise functionals ⋮ Annihilation-derivative, creation-derivative and representation of quantum martingales ⋮ DIAGONALIZATION OF THE LÉVY LAPLACIAN AND RELATED STABLE PROCESSES ⋮ \(\gamma\)-quantum product of white noise operators and applications ⋮ HIERARCHY OF LÉVY–LAPLACIANS AND QUANTUM STOCHASTIC PROCESSES ⋮ Quantum stochastic differential equations in terms of quantum white noise ⋮ INTEGRAL REPRESENTATION OF QUANTUM MARTINGALES ⋮ Stochastic Processes Associated with a Sum of the Lévy Laplacians ⋮ QUANTUM STOCHASTIC ANALYSIS VIA WHITE NOISE OPERATORS IN WEIGHTED FOCK SPACE ⋮ Quantum stochastic integral representations of Fock space operators ⋮ Higher Powers of Quantum White Noises in Terms of Integral Kernel Operators

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