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General relativity from gauge invariance

Published online by Cambridge University Press:  24 October 2008

Eric A. Lord
Eric A. Lord
Affiliation:
Department of Theoretical Physics, University of Durham
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Abstract

The free field equations for particles with spin are invariant under a group SL(2, c) whose transformations correspond to changes of representation of the twocomponent spinor algebra. The generalization of the equations which extends this invariance to a guage invariance in the Yang–Mills sense necessitates the introduction of auxiliary fields (which are also necessary to maintain Lorentz covariance). These fields can be interpreted as the potentials of a spin-2 field, just as the auxiliary fields for the charge gauge group are the potentials of a spin-l field (electromagnetism); this spin-2 field is then self-interacting. The Bargmann–Wigner formulation of the linear spin-2 field, when modified by the proposed self-interaction, yields a non-linear theory of a spin-2 field which is shown to be identical with Einstein's gravitational theory. With this interpretation the auxiliary fields take on an extra role of Yang–Mills field for the general coordinate transformation group – that is, they are the components of the affine connexion.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 3 , May 1971 , pp. 423 - 442
Copyright
Copyright © Cambridge Philosophical Society 1971

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