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

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

1998-06-11

arxiv.org/abs/hep-th/9806085v3

Phys.Rev. D58 (1998) 106004

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 42 pages. v2 improvements in AdS section. In v3 sec.6.2 is modified; the more general potential is limited to a smaller

Scientific paper

10.1103/PhysRevD.58.106004

We show that a simple OSp(1/2) worldline gauge theory in 0-brane phase space (X,P), with spin degrees of freedom, formulated for a d+2 dimensional spacetime with two times X^0,, X^0', unifies many physical systems which ordinarily are described by a 1-time formulation. Different systems of 1-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, 2-time physics unifies an infinite number of 1-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 n of spinning degrees of freedom the gauge group changes to OSp(n/2). Then the eigenvalue of the Casimirs of SO(d,2) depend on n and then the content of the 1-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.

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