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The search for new representations of the Wheeler-DeWitt equation using the first order formalism

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Abstract

We obtain all possible representations of the Wheeler-DeWitt equation that may arise from the development of the first-order formalism for the quantization of gravity. They are the usual one, the modified extrinsic curvature representation and the intrisic and extrinsic time representations, which arise naturally in this formalism. We show that in the intrinsic time representation the factor-ordering problem is restricted to the pair consisting of the determinant of the metric of the spacelike hypersurfaces and its canonical momentum. Contrary to what was suggested in an earlier paper, no new representations can be obtained in this formalism or by considering actions differing by a total divergence.

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Authors and Affiliations

  1. Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud 150, cep 22290-180, Rio de Janeiro, RJ, Brazil

    N. Pinto-Neto & A. F. Velasco

  2. Laboratoire de Gravitation et Cosmologie Relativistes, Tour 22/12, Université P. et M. Curie, 4 pl. Jussieu, Paris Cedex 05, France

    N. Pinto-Neto

Authors
  1. N. Pinto-Neto
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  2. A. F. Velasco
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Pinto-Neto, N., Velasco, A.F. The search for new representations of the Wheeler-DeWitt equation using the first order formalism. Gen Relat Gravit 25, 991–1007 (1993). https://doi.org/10.1007/BF00763550

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  • DOI: https://doi.org/10.1007/BF00763550

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