Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1996-04-04
Annals of Phys. (N.Y.) 241 (1995) 50
Physics
High Energy Physics
High Energy Physics - Phenomenology
Scientific paper
By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg algebra, $q$-WH, into the theory of entire analytic functions. The $q$--WH algebra operators are realized in terms of finite difference operators in the $z$ plane. In order to exhibit the relevance of our study, several applications to different cases of physical interest are discussed: squeezed states and the relation between coherent states and theta functions on one side, lattice quantum mechanics and Bloch functions on the other, are shown to find a deeper mathematical understanding in terms of $q$-WH. The r\^ole played by the finite difference operators and the relevance of the lattice structure in the completeness of the coherent states system suggest that the quantization of the WH algebra is an essential tool in the physics of discretized (periodic) systems.
Celeghini Enrico
de Martino Salvatore
Rasetti Mario
Siena Silvio de
Vitiello Giuseppe
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