Gauged duality, conformal symmetry, and spacetime with two times

Journal Article · Tue Sep 01 04:00:00 EDT 1998 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.58.066004· OSTI ID:641701

Bars, I; Deliduman, C; Andreev, O ^[1]

---

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

We construct a duality between several simple physical systems by showing that they are different aspects of the same quantum theory. Examples include the free relativistic massless particle and the hydrogen atom in any number of dimensions. The key is the gauging of the Sp(2) duality 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{sup {mu}},p{sup {mu}} get enlarged by one additional spacelike and one additional timelike dimension to (x{sup M},p{sup M}). A manifest global symmetry SO(d,2) rotates (x{sup M},p{sup 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 one gauge or as the dynamical symmetry of a totally different physical system in another gauge. Thanks to the gauge symmetry, the theory permits various choices of {open_quotes}time{close_quotes} 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 with a gauged duality symmetry that produces appropriate constraints. {copyright} {ital 1998} {ital The American Physical Society}

• OSTI ID: 641701
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 6 Vol. 58; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CONFORMAL INVARIANCE
DUALITY
GAUGE INVARIANCE
GLOBAL ANALYSIS
HAMILTONIANS
HYDROGEN
MASSLESS PARTICLES
MINKOWSKI SPACE
PHASE SPACE
SO GROUPS
SP GROUPS
SPACE-TIME