Coherent states on the circle
  A careful study of the physical properties of a family of coherent states on the circle, introduced some years ago by de Bi\`evre and Gonz\'alez in [DG 92], 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 labeled by the points of the cylinder $S^1 \times \R$, 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. 
Jose A. Gonzalez and Mariano A. del Olmo