The Ito algebra of quantum Gaussian fields

DOI10.1016/0022-1236(89)90036-0zbMath0669.60099OpenAlexW2115782887MaRDI QIDQ1118919

Luigi Accardi, Johan Quaegebeur

Publication date: 1989

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2108/82408

zbMATH Keywords

Fock representationannihilationfinitely additive measurecreationmutual quadratic variationquantum Gaussian fields

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Stochastic mechanics (including stochastic electrodynamics) (81P20) Stochastic analysis (60H99)

Related Items (9)

The Ito algebra of quantum Gaussian fields ⋮ The weak coupling limit as a quantum functional central limit ⋮ Squeezing noises as weak coupling limit of Hamiltonian system ⋮ A quantum nonadapted Ito formula and stochastic analysis in Fock scale ⋮ A representation free quantum stochastic calculus ⋮ A quantum nonadapted Ito formula and stochastic analysis in Fock scale ⋮ The Unitarity Conditions for the Square of White Noise ⋮ A Fermion Lévy theorem ⋮ White Noise Approach to stochastic integration

Cites Work

• Quantum Ito's formula and stochastic evolutions
• Quasi-free quantum stochastic integrals for the CAR and CCR
• Fermion Ito's formula and stochastic evolutions
• The Ito algebra of quantum Gaussian fields
• A representation free quantum stochastic calculus
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