Gauge symmetry in phase space with spin, a basis for conformal symmetry and duality among many interactions

Publisher Website
Google Scholar
Abstract
We show that a simple OSp(1/2) world line gauge theory in O-brane phase space X-M(tau),P-M(tau) with spin degrees of freedom psi(M)(tau), formulated 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 emerge by choosing gauges that embed ordinary time in d + 2 dimensions in different ways. The embeddings have different topology and geometry for the choice of time among the d + 2 dimensions. Thus, two-time physics unifies an infinite number of one-time physical interacting systems, and establishes a kind of duality among them. One manifestation of the two times is that all of these physical systems have the same quantum Hilbert space in the form of a unique representation of SO(d,2) with the same Casimir eigenvalues. By changing the number of spinning degrees 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 Casimir 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 on n. The models we study raise new questions about the nature of spacetime. [S0556-2821(98)05620-3].