FRAMES, THE BETA-DUALITY IN MINKOWSKI SPACE AND SPIN COHERENT STATES

In the spirit of some earlier work on building coherent states for the Poincare group in one space and one time dimension, we construct here analogous families of states for the full Poincare group, for represe ntations corresponding to mass m > 0 and arbitrary integral or half-in tegral spin. Each family of coherent states is defined by an affine se ction in the group and constitutes a frame. The sections, in their tur n, are determined by particular velocity vector fields, the latter alw ays appearing in dual pairs. Geometrically, each family of coherent st ates is related to the choice of a Riemannian structure on the forward mass hyperboloid or, equivalently, to the choice of a certain paralle l bundle in the relativistic phase space. The large variety of coheren t states obtained tempts us to believe that there is rich scope here f or application to spin-dependent problems in atomic and nuclear physic s, as well as to image reconstruction problems, using the discretized versions of these frames.