CANONICAL COHERENT STATES FOR THE RELATIVISTIC HARMONIC-OSCILLATOR

In this paper there are constructed manifestly covariant relativistic coherent states on the entire complex plane which reproduce others pre viously introduced on a given SL(2,R) representation, once a change of variables z is an element of C --> z(D) is an element of E unit disk is performed. Also introduced are higher-order, relativistic creation and annihilation operators, (z) over cap,(z) over cap dagger with cano nical commutation relation [(a) over cap, (a) over cap dagger] = 1 rat her than the covariant one [(z) over cap, (z) over cap dagger] approxi mate to energy and naturally associated with the SL(2,R) group. The ca nonical (relativistic) coherent states are then defined as eigenstates of (a) over cap. Finally, a canonical, minimal representation is cons tructed in configuration space by means of eigenstates of a canonical position operator. (C) 1995 American Institute of Physics.