GAUGED DUALITY, CONFORMAL SYMMETRY, AND SPACETIME WITH 2 TIMES - ART.NO. 066004

We construct a duality between several simple physical systems by show ing that they are different aspects of the same quantum theory. Exampl es include the free relativistic massless particle and the hydrogen at om in any number of dimensions. The key is the gauging of the Sp(2) du ality symmetry that treats position and momentum (x,p) as a doublet in phase space. As a consequence of the gauging, the Minkowski spacetime vectors x(mu),p(mu) get enlarged by one additional spacelike and one additional timelike dimension to (x(M),p(M)). A manifest global symmet ry SO(d,2) rotates (x(M),p(M))-like (d+2)-dimensional vectors. The SO( d,2) symmetry of the parent theory may be interpreted as the familiar conformal symmetry of quantum field theory in Minkowski spacetime in o ne gauge or as the dynamical symmetry of a totally different physical system in another gauge. Thanks to the gauge symmetry, the theory perm its various choices of ''time'' which correspond to different looking Hamiltonians, while avoiding ghosts. Thus we demonstrate that there is a physical role for a spacetime with two times when taken together wi th a gauged duality symmetry that produces appropriate constraints. [S 0556-2821(98)04016-8].