Year: 1998
Type: article
Abstract: 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 ${x}^{\ensuremath{\mu}}{,p}^{\ensuremath{\mu}}$ get enlarged by one additional spacelike and one additional timelike dimension to ${(x}^{M}{,p}^{M}).$ A manifest global symmetry $\mathrm{SO}(d,2)$ rotates ${(x}^{M}{,p}^{M})$-like $(d+2)$-dimensional vectors. The $\mathrm{SO}(d,2)$ 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 ``time'' 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.
Authors: I. Bars, C. Deliduman, O. Andreev
Institution: University of Southern California
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: U.S. Department of Energy
OpenAlex ID: W2084096838