Normal Biconformal Spaces

Details Normal Biconformal Spaces Normal Biconformal Spaces

1997-06-29

arxiv.org/abs/hep-th/9706215v1

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, plain TeX, no figures

Scientific paper

A new 8-dimensional conformal gauging avoids the unphysical size change, third order gravitational field equations, and auxiliary fields that prevent taking the conformal group as a fundamental symmetry. We give the structure equations, gauge transformations and intrinsic metric structure for the new biconformal spaces. We prove that a torsion-free biconformal space with exact Weyl form, closed dilational curvature and trace-free spacetime curvature admits a sub-bundle of vanishing Weyl form homeomorphic to the Whitney sum bundle of the tangent bundle and the bundle of orthonormal Lorentz frames over 4-dimensional spacetime. Conversely, any 4-dimensional spacetime extends uniquely to such a normal biconformal space. The Einstein equation holds if and only if the biconformal basis is orthonormal. Unconstrained antisymmetric trace of the spacetime curvature provides a closed 2-form, independent of the Weyl vector, consistently interpretable as the electromagnetic field. The trace of the spacetime co-torsion decouples from gravitational sources and serves as electromagnetic source.

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