F eb 2 00 3 Representation of Semigroups in Rigged Hilbert Spaces : Subsemigroups of the Weyl - Heisenberg Group

ar X iv : q ua nt - p h / 03 10 14 7 v 1 2 3 O ct 2 00 3 REPRESENTATIONS OF COHERENT STATES IN NON - ORTHOGONAL BASES

Starting with the canonical coherent states, we demonstrate that all the so-called nonlinear coherent states, used in the physical literature, as well as large classes of other generalized coherent states, can be obtained by changes of bases in the underlying Hilbert space. This observation leads to an interesting duality between pairs of generalized coherent states, bringing into play a Gelfan...

A Necessary Condition for Weyl-Heisenberg Frames

ar X iv : h ep - t h / 93 10 05 4 v 2 3 F eb 1 99 4 Hilbert Spaces for Nonrelativistic and Relativistic “ Free ” Plektons ( Particles with Braid Group Statistics ) ∗

Using the theory of fibre bundles, we provide several equivalent intrinsic descriptions for the Hilbert spaces of n “free” nonrelativistic and relativistic plektons in two space dimensions. These spaces carry a ray representation of the Galilei group and a unitary representation of the Poincaré group respectively. In the relativistic case we also discuss the situation where the braid group is r...

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

THE LEFT REGULAR REPRESENTATION OF A COMMUTATIVE SEPARATIVE SEMIGROUP

In this paper, a commutative semigroup will be written as a disjoint union of its cancellative subsemigroups. Based on this fact we will define the left regular representation of a commutative separative semigroup and show that this representation is faithful. Finally concrete examples of commutative separative semigroups, their decompositions and their left regular representations are given.