A GENERAL THEOREM ON SQUARE-INTEGRABILITY - VECTOR COHERENT STATES

We derive a generalization of the well-known theorem for the square in tegrability of a unitary irreducible representation of a locally compa ct group. The generalization covers the case of representations admitt ing vector coherent states. The result is illustrated by an example dr awn from the isochronous Galilei group. The construction yields a wide variety of coherent states, labeled by phase space points, which sati sfy a resolution of the identity condition, and incorporate spin degre es of freedom. (C) 1998 American Institute of Physics. [S0022-2488(98) 00108-X].