COHERENT STATES ON THE CIRCLE

A careful study of the physical properties of a family of coherent sta tes an the circle, introduced some years ago by de Bievre and Gonzalez (in 1992 Semiclassical behaviour of the Weyl correspondence on the ci rcle Group Theoretical Methods in Physics vol I (Madrid: Ciemat)), is carried out. They were obtained from the Weyl-Heisenberg coherent stat es in L-2(R) by means of the Weil-Brezin-Zak transformation, they are labelled by the points of the cylinder S-1 x R, and they provide a rea lization of L-2(S-1) by entire functions(similar to the well known Foc k-Bargmann construction). In particular, we compute the expectation va lues of the position and momentum operators on the circle and we discu ss the Heisenberg uncertainty relation.