Time-orthogonal unitary dilations and noncommutative Feynman-Kac formulae

DOI10.1007/BF01976044zbMath0485.46038OpenAlexW3037710339MaRDI QIDQ1164242

K. R. Parthasarathy, Robin L. Hudson, Patrick D. F. Ion

Publication date: 1982

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01976044

zbMATH Keywords

Wiener measurecocyclesecond quantisationconditional expectation of a two parameter unitary evolutionnoncommutative Feynman-Kac formulaeself-adjoint contraction one-parameter semigrouptime orthogonal unitary dilation

Mathematics Subject Classification ID

Groups and semigroups of linear operators (47D03) Applications of selfadjoint operator algebras to physics (46L60) Stochastic mechanics (including stochastic electrodynamics) (81P20)

Related Items (14)

Feynman-Kac representation of some noncommutative elliptic operators ⋮ On characterizing quantum stochastic evolutions ⋮ The Ito-Clifford integral ⋮ Classical and quantum probability ⋮ Algebraic theory of product integrals in quantum stochastic calculus ⋮ QUANTUM STOCHASTIC CALCULUS ON BOOLEAN FOCK SPACE ⋮ Quantum stochastic processes ⋮ FEYNMAN–KAC REPRESENTATION AND MARKOV PROPERTY OF SEMIGROUPS GENERATED BY NONCOMMUTATIVE ELLIPTIC OPERATORS ⋮ On quantum stochastic differential equations with unbounded coefficients ⋮ Quantum Ito's formula and stochastic evolutions ⋮ Fermion Ito's formula and stochastic evolutions ⋮ Time-orthogonal unitary dilations and noncommutative Feynman-Kac formulae. II ⋮ Before thy throne I slip in gently, hoping nobody will notice: A memorial to Robin Hudson (1940–2021) ⋮ Quantum stochastic calculus, operation valued stochastic processes, and continual measurements in quantum mechanics

Cites Work

• Quantum mechanical Wiener processes
• Symmetric Hilbert spaces and related topics. Infinitely divisible positive definite functions, continuous products and tensor products, Gaussian and Poissonian stochastic processes
• Semi-Groups of Measures on Lie Groups
• On the quantum Feynman-Kac formula
• Some contraction semigroups in quantum probability
• Scattering theory
• Quantum stochastic processes
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