QUANTUM GROUPS, COHERENT STATES, SQUEEZING AND LATTICE QUANTUM-MECHANICS

By resorting to the Fock-Bargmann representation, we incorporate the q uantum Weyl-Heisenberg algebra, q-WH, into the theory of entire analyt ic functions. The q-WH algebra operators are realized in terms of fini te difference operators in the z plane. In order to exhibit the releva nce of our study, several applications to different cases of physical interest are discussed; squeezed states and the relation between coher ent states and theta functions on one side, and lattice quantum mechan ics and Bloch functions on the other, are shown to find a deeper mathe matical understanding in terms of q-WH. The role played by the finite difference operators and the relevance of the lattice structure in the completeness of the coherent states system suggest that the quantizat ion of the WH algebra is an essential tool in the physics of discretiz ed (periodic) systems. (C) 1995 Academic Press, Inc.