Gravity, two times, tractors, Weyl invariance, and six-dimensional quantum mechanics

Journal Article · Wed Sep 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.064037· OSTI ID:21421179

Bonezzi, R ^[1]; Latini, E ^[2]; Waldron, A ^[3]

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1. Dipartimento di Fisica, Universita di Bologna, via Irnerio 46, I-40126 Bologna (Italy) and INFN sezione di Bologna, via Irnerio 46, I-40126 Bologna (Italy)
2. INFN, Laboratori Nazionali di Frascati, CP 13, I-00044 Frascati (Italy)
3. Department of Mathematics, University of California, Davis California 95616 (United States)

Fefferman and Graham showed some time ago that four-dimensional conformal geometries could be analyzed in terms of six-dimensional, ambient, Riemannian geometries admitting a closed homothety. Recently, it was shown how conformal geometry provides a description of physics manifestly invariant under local choices of unit systems. Strikingly, Einstein's equations are then equivalent to the existence of a parallel scale tractor (a six-component vector subject to a certain first order covariant constancy condition at every point in four-dimensional spacetime). These results suggest a six-dimensional description of four-dimensional physics, a viewpoint promulgated by the 2 times physics program of Bars. The Fefferman-Graham construction relies on a triplet of operators corresponding, respectively, to a curved six-dimensional light cone, the dilation generator and the Laplacian. These form an sp(2) algebra which Bars employs as a first class algebra of constraints in a six-dimensional gauge theory. In this article four-dimensional gravity is recast in terms of six-dimensional quantum mechanics by melding the 2 times and tractor approaches. This parent formulation of gravity is built from an infinite set of six-dimensional fields. Successively integrating out these fields yields various novel descriptions of gravity including a new four-dimensional one built from a scalar doublet, a tractor-vector multiplet and a conformal class of metrics.

• OSTI ID: 21421179
• Journal Information: Physical Review. D, Particles Fields, Vol. 82, Issue 6; Other Information: DOI: 10.1103/PhysRevD.82.064037; (c) 2010 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
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EINSTEIN FIELD EQUATIONS
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GAUGE INVARIANCE
GRAVITATION
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SPACE-TIME