Higher Powers of Quantum White Noises in Terms of Integral Kernel Operators

DOI10.1142/S0219025798000296zbMath0928.60088OpenAlexW2031533830MaRDI QIDQ4236705

Nobuaki Obata, Dong Myung Chung, Un Cig Ji

Publication date: 9 January 2000

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/s0219025798000296

zbMATH Keywords

interacting random processesquantum stochastic calculus

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Quantum stochastic calculus (81S25)

Related Items (11)

Analytic characterizations of infinite dimensional distributions ⋮ Higher powers of analytical operators and associated ∗-Lie algebras ⋮ ANALYTIC CHARACTERIZATION OF GENERALIZED FOCK SPACE OPERATORS AS TWO-VARIABLE ENTIRE FUNCTIONS WITH GROWTH CONDITION ⋮ \(\gamma\)-quantum product of white noise operators and applications ⋮ Stochastic integral representation theorem for quantum semimartingales. ⋮ A Unified Characterization Theorem in White Noise Theory ⋮ QUANTUM STOCHASTIC ANALYSIS VIA WHITE NOISE OPERATORS IN WEIGHTED FOCK SPACE ⋮ AN EXTENDED STOCHASTIC INTEGRAL AND A WICK CALCULUS ON PARAMETRIZED KONDRATIEV-TYPE SPACES OF MEIXNER WHITE NOISE ⋮ Quantum stochastic calculus associated with quadratic quantum noises ⋮ Characterization of S-transform for general construction of infinite-dimensional distributions ⋮ Multi-parameter transformation groups on white noise functionals

Cites Work

• Quantum Ito's formula and stochastic evolutions
• Rotation-invariant operators on white noise functionals
• Calculus on Gaussian white noise. I
• An analytic characterization of symbols of operators on white noise functionals
• Operator calculus on vector-valued white noise functionals
• Integral kernel operators on Fock space. -- Generalizations and applications to quantum dynamics
• Quantum stochastic positive evolutions: Characterization, construction, dilation
• Transformations on white noise functions associated with second order differential operators of diagonal type
• Quantum white noises—White noise approach to quantum stochastic calculus
• Infinite dimensional rotations and Laplacians in terms of white noise calculus
• Quantum White Noises and Free Fields
• A New Class of White Noise Generalized Functions

This page was built for publication: Higher Powers of Quantum White Noises in Terms of Integral Kernel Operators