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


L. Accardi and A. Boukas

Centro Vito Volterra, Universitą di Roma Tor Vergata,
via Columbia 2, 00133 Roma,

Department of Mathematics,
American College of Greece,
Aghia Paraskevi, Athens 15342,


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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