GAUGE-SYMMETRY IN PHASE-SPACE WITH SPIN, A BASIS FOR CONFORMAL SYMMETRY AND DUALITY AMONG MANY INTERACTIONS - ART. NO. 106004

We show that a simple OSp(1/2) world line gauge theory in O-brane phas e space X-M(tau),P-M(tau) with spin degrees of freedom psi(M)(tau), fo rmulated for a (d + 2)-dimensional spacetime with two times X-0(tau),X -0'(tau), unifies many physical systems which ordinarily are described by a one-time formulation. Different systems of one-time physics emer ge by choosing gauges that embed ordinary time in d + 2 dimensions in different ways. The embeddings have different topology and geometry fo r the choice of time among the d + 2 dimensions. Thus, two-time physic s unifies an infinite number of one-time physical interacting systems, and establishes a kind of duality among them. One manifestation of th e two times is that all of these physical systems have the same quantu m Hilbert space in the form of a unique representation of SO(d,2) with the same Casimir eigenvalues. By changing the number of spinning degr ees of freedom sigma(a)(M)(tau), a = 1,2,...,n (including no spin n = 0), the gauge group changes to OSp(n/2). Then the eigenvalue of the Ca simir operators of SO(d,2) depend on n and the content of the one-time physical systems that are unified in the same representation depend o n n. The models we study raise new questions about the nature of space time. [S0556-2821(98)05620-3].