Coherent states on the circle

A careful study of the physical properties of a family of coherent states an the circle, introduced some years ago by de Bievre and Gonzalez (in 1992 Semiclassical behaviour of the Weyl correspondence on the circle Group Theoretical Methods in Physics vol I (Madrid: Ciemat)), is carried out. They were obtained from the Weyl-Heisenberg coherent states 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 realization of L-2(S-1) by entire functions(similar to the well known Fock-Bargmann construction). In particular, we compute the expectation values of the position and momentum operators on the circle and we discuss the Heisenberg uncertainty relation.