Poincaré and de Sitter gauge theories of gravity with propagating torsion

A. A. Tseytlin
Phys. Rev. D 26, 3327 – Published 15 December 1982
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Abstract

We consider a gauge approach to the gravitational theory based on the local Poincaré P10 or de Sitter S10 groups. The P10 gauge rotations and translations take place in the tangent spaces to the space-time manifold. We interpret the independence of matter fields from the tangent vectors as the necessity to use a nonlinear realization of the P10 or S10 groups thus effectively breaking the full symmetry to the Lorentz group. The Lagrangian we choose is the S10 Yang-Mills invariant with the space-time metric expressed in terms of the translational part of the S10 nonlinear gauge field. Various consequences of the theory are discussed, including the correspondence with general relativity, the propagating spin-connection interactions, the analogy with the chiral Higgs mechanism, instantonlike solutions, a possibility of gravitational repulsion due to the noncompactness of the Lorentz group, etc. We also analyze the quantization of the theories with torsion with special emphasis on the presence of the nonlinear realization. We stress the possibility of obtaining a renormalizable theory if the metric is not quantized but is expressed in terms of a mean value of the quantized S10 nonlinear gauge field.

  • Received 12 November 1981

DOI:https://doi.org/10.1103/PhysRevD.26.3327

©1982 American Physical Society

Authors & Affiliations

A. A. Tseytlin

  • Department of Theoretical Physics, P. N. Lebedev Physical Institute, USSR Academy of Sciences, Leninsky Pr. 53, Moscow 117924, USSR

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Vol. 26, Iss. 12 — 15 December 1982

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