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

Journal Article · Sun Nov 01 04:00:00 EST 1998 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.58.106004· OSTI ID:664752

Bars, I; Deliduman, C ^[1]

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1. Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089-0484 (United States)

We show that a simple OSp(1/2) world line gauge theory in 0-brane phase space X{sup M}({tau}),P{sup M}({tau}) with spin degrees of freedom {psi}{sup M}({tau}), formulated for a (d+2)-dimensional spacetime with two times X{sup 0}({tau}),X{sup 0{prime}}({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 {psi}{sub a}{sup M}({tau}), a=1,2,{hor_ellipsis},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. {copyright} {ital 1998} {ital The American Physical Society}

• OSTI ID: 664752
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 10 Vol. 58; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CASIMIR OPERATORS
CONFORMAL MAPPING
DUALITY
PHASE SPACE
UNIFIED GAUGE MODELS