Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-10-20
Ann.Phys.241:50-67,1995
Physics
High Energy Physics
High Energy Physics - Theory
22 pages, TEX file, DFF188/9/93 Firenze
Scientific paper
10.1006/aphy.1995.1055
By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg ($q$-WH) algebra into the theory of entire analytic functions. The main tool is the realization of the $q$--WH algebra in terms of finite difference operators. The physical relevance of our study relies on the fact that coherent states (CS) are indeed formulated in the space of entire analytic functions where they can be rigorously expressed in terms of theta functions on the von Neumann lattice. The r\^ole played by the finite difference operators and the relevance of the lattice structure in the completeness of the CS system suggest that the $q$--deformation of the WH algebra is an essential tool in the physics of discretized (periodic) systems. In this latter context we define a quantum mechanics formalism for lattice systems.
Celeghini
de Martino Salvatore
Rasetti Mario
Siena Silvio de
Vitiello Giuseppe
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