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    Kim, Sang-Woo and Pak, D G 2008. Torsion as a dynamic degree of freedom of quantum gravity. Classical and Quantum Gravity, Vol. 25, Issue. 6, p. 065011.

    Hehl, Friedrich W. von der Heyde, Paul Kerlick, G. David and Nester, James M. 1976. General relativity with spin and torsion: Foundations and prospects. Reviews of Modern Physics, Vol. 48, Issue. 3, p. 393.

    Lord, Eric A 1975. On energy-momentum tensors as sourcesof spin-2 fields. Pramana, Vol. 5, Issue. 1, p. 29.

    Lord, E. A. Sivaram, C. and Sinha, K. P. 1974. f-gravity and the proton-electron mass ratio. Lettere Al Nuovo Cimento Series 2, Vol. 11, Issue. 2, p. 142.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 69, Issue 3
  • May 1971, pp. 423-442

General relativity from gauge invariance

  • Eric A. Lord (a1)
  • DOI:
  • Published online: 24 October 2008

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.

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