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Conformal invariance and torsion in general relativity

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Abstract

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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Author notes

  1. José W. Maluf

    Present address: Departamento de Física, Universidade de Brasília, 70.910, Brasília, D. F., Brazil

Authors and Affiliations

  1. Department of Physics and Astronomy, University of Rochester, 14627, Rochester, New York

    José W. Maluf

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  1. José W. Maluf
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Maluf, J.W. Conformal invariance and torsion in general relativity. Gen Relat Gravit 19, 57–71 (1987). https://doi.org/10.1007/BF01119811

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