Conformal invariance and torsion in general relativity.

Details Conformal invariance and torsion in general relativity. Conformal invariance and torsion in general relativity.

Jan 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987gregr..19...57m&link_type=abstract

General Relativity and Gravitation, Volume 19, Issue 1, pp.57-71

Physics

6

General Relativity

Scientific paper

We study a theory for gravity in which the linear connections are assumed to be arbitrary, except that they are restricted to satisfy the metric condition ∇μ g λν=0. A scalar field is added to the theory, and a conformally invariant action integral, linear in the curvature tensor, is defined. The linear connections emerging from the variational principle contain torsion that is related to a propagating spin-1 vector field, identified as the electromagnetic gauge potential. We obtain a set of conformally invariant equations for the metric field, and conclude that Einstein's equations arise from a particular choice of gauge. Finally, spin-1/2 fields are introduced by means of the vierbein formalism, and the qualitative features of the theory are maintained.

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