


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 nontrivial central extensions of the Heisenberg algebra, generated by elements and E satisfying the commutation relations , and , where a and are dual, h is selfadjoint, E is the nonzero selfadjoint 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 selfadjoint operator
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