Frames, the beta-duality in Minkowski space and spin coherent states
Document Type
Article
Publication Date
9-7-1996
Abstract
In the spirit of some earlier work on building coherent states for the Poincaré group in one space and one time dimension, we construct here analogous families of states for the full Poincaré group, for representations corresponding to mass m > 0 and arbitrary integral or half-integral spin. Each family of coherent states is defined by an affine section in the group and constitutes a frame. The sections, in their turn, are determined by particular velocity vector fields, the latter always appearing in dual pairs. Geometrically, each family of coherent states is related to the choice of a Riemannian structure on the forward mass hyperboloid or, equivalently, to the choice of a certain parallel bundle in the relativistic phase space. The large variety of coherent states obtained tempts us to believe that there is rich scope here for application to spin-dependent problems in atomic and nuclear physics, as well as to image reconstruction problems, using the discretized versions of these frames. © 1996 IOP Publishing Ltd.
Keywords
Relativistic hydrogen-atom, Unified treatment, Green-functions, Poincare group, Phase-space, Representation
Divisions
fac_eng
Publication Title
Journal of Physics a-Mathematical and General
Volume
29
Issue
17
Additional Information
Vg656 Times Cited:3 Cited References Count:22