Representations of Lie superalgebras and generalized boson-fermion equivalence in quantum stochastic calculus

1997 ◽  
Vol 186 (1) ◽  
pp. 87-94 ◽  
Author(s):  
T. M. W. Eyre ◽  
R. L. Hudson
Keyword(s):  
Stochastic Calculus ◽  
Lie Superalgebras ◽  
Quantum Stochastic 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

scholarly journals Quantum stochastic calculus approach to modeling double-pass atom-field coupling

2008 ◽  
Vol 78 (2) ◽  
Author(s):  
Gopal Sarma ◽  
Andrew Silberfarb ◽  
Hideo Mabuchi
Keyword(s):  
Stochastic Calculus ◽  
Double Pass ◽  
Quantum Stochastic Calculus ◽  
Field Coupling

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.

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