The Australian Journal of Mathematical Analysis and Applications


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ISSN 1449-5910  

 

Paper Information

Paper Title:

On the Fock Representation of the Central Extensions of the Heisenberg Algebra

Author(s):

L. Accardi and A. Boukas

Centro Vito Volterra, Universitą di Roma Tor Vergata,
via Columbia 2, 00133 Roma,
Italy
accardi@volterra.mat.uniroma2.it 
URL: http://volterra.mat.uniroma2.it

Department of Mathematics,
American College of Greece,
Aghia Paraskevi, Athens 15342,
Greece
andreasboukas@acg.edu

Abstract:

We examine the possibility of a direct Fock representation of the recently obtained non-trivial central extensions of the Heisenberg algebra, generated by elements and E satisfying the commutation relations ,  and , where a and are dual, h is self-adjoint, E is the non-zero self-adjoint central element and We define the exponential vectors associated with the Fock space, we compute their Leibniz function (inner product), we describe the action of a, and h on the exponential vectors and we compute the moment generating and characteristic functions of the classical random variable corresponding to the self-adjoint operator

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