Some New Examples of Lie Super-Algebra Representations Arising from Quantum Stochastic Calculus

1998 ◽  
Vol 01 (01) ◽  
pp. 33-42
Author(s):  
K. R. Parthasarathy
Keyword(s):  
Stochastic Calculus ◽  
Stochastic Integrals ◽  
Quantum Stochastic Calculus

Following the methods of Refs. 1 and 2 we construct here a family of Lie super-algebra representations in terms of quantum stochastic integrals.

Wick Calculus of Generalized Operators and its Applications to Quantum Stochastic Calculus

1998 ◽  
Vol 01 (03) ◽  
pp. 455-466 ◽  
Author(s):  
Zhiyuan Huang ◽  
Shunlong Luo
Keyword(s):  
Differential Equations ◽  
White Noise ◽  
Stochastic Analysis ◽  
Stochastic Calculus ◽  
Stochastic Integrals ◽  
Algebra Structure ◽  
Quantum Stochastic Calculus ◽  
Fundamental Properties ◽  
White Noise Calculus ◽  
Wick Calculus

A nonlinear and stochastic analysis of free Bose field is established in the framework of white noise calculus. Wick algebra structure is introduced in the space of generalized operators generated by quantum white noise, some fundamental properties of the calculus based on the Wick algebra are investigated. As applications, quantum stochastic integrals and quantum stochastic differential equations are treated from the viewpoint of Wick calculus.

scholarly journals A representation free quantum stochastic calculus

1992 ◽  
Vol 104 (1) ◽  
pp. 149-197 ◽  
Author(s):  
L Accardi ◽  
F Fagnola ◽  
J Quaegebeur
Keyword(s):  
Stochastic Calculus ◽  
Quantum Stochastic Calculus

Infinite degrees of freedom Weyl representation: Characterization and application

2018 ◽  
Vol 21 (01) ◽  
pp. 1850002
Author(s):  
Abdessatar Barhoumi ◽  
Bilel Kacem Ben Ammou ◽  
Hafedh Rguigui
Keyword(s):  
Degrees Of Freedom ◽  
Explicit Construction ◽  
Stochastic Calculus ◽  
Generalized Functions ◽  
Academic Press ◽  
Quantum Stochastic Calculus ◽  
Fock Representation ◽  
Infinite Dimensional ◽  
Weyl Representation ◽  
Nuclear Spaces

By means of infinite-dimensional nuclear spaces, we generalize important results on the representation of the Weyl commutation relations. For this purpose, we construct a new nuclear Lie group generalizing the groups introduced by Parthasarathy [An Introduction to Quantum Stochastic Calculus (Birkhäuser, 1992)] and Gelfand–Vilenkin [Generalized Functions (Academic Press, 1964)] (see Ref. 15). Then we give an explicit construction of Weyl representations generated from a non-Fock representation. Moreover, we characterize all these Weyl representations in quantum white noise setting.

Sign in / Sign up

Export Citation Format

Share Document