Conformal symmetry and duality between free particle, H atom, and harmonic oscillator

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

DOI:https://doi.org/10.1103/PhysRevD.58.066006· OSTI ID:641703

Bars, I ^[1]

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

We establish a duality between the free massless relativistic particle in d dimensions, the non-relativistic hydrogen atom (1/r potential) in (d{minus}1) space dimensions, and the harmonic oscillator in (d-2) space dimensions with its mass given as the light cone momentum of an additional dimension. The duality is in the sense that the classical action of these systems are gauge fixed forms of the same worldline gauge theory action at the classical level, and they are all described by the same unitary representation of the conformal group SO (d,2) at the quantum level. The world line action has a gauge symmetry Sp(2) which treats canonical variables (x,p) as doublets and exists only with a target spacetime that has d spacelike dimensions and two timelike dimensions. This spacetime is constrained due to the gauge symmetry, and the various dual solutions correspond to solutions of the constraints with different topologies. For example, for the H atom the two timelike dimensions X{sup 0{sup {prime}}},X{sup 0} live on a circle. The model provides an example of how realistic physics can be viewed as existing in a larger covariant space that includes two timelike coordinates, and how the covariance in the larger space unifies different looking physics into a single system. {copyright} {ital 1998} {ital The American Physical Society}

• OSTI ID: 641703
• 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
HARMONIC OSCILLATORS
RELATIVISTIC RANGE
SO GROUPS
SP GROUPS
SPACE-TIME
TOPOLOGY
UNITARITY