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The Reduced Phase Space of Palatini–Cartan–Holst Theory

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Abstract

General relativity in four dimensions can be reformulated as a gauge theory, referred to as Palatini–Cartan–Holst theory. This paper describes its reduced phase space using a geometric method due to Kijowski and Tulczyjew and its relation to that of the Einstein–Hilbert approach.

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Acknowledgements

We thank Giovanni Canepa for several constructive discussions, and Friedrich Hehl for valuable comments about the controversy in the nomenclature. We thank G. Canepa and the anonymous referee for having found flaws in previous versions of the article.

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Authors and Affiliations

  1. Institut für Mathematik, Winterthurerstrasse 190, 8057, Zurich, Switzerland

    Alberto S. Cattaneo

  2. Department of Mathematics, University of California, Berkeley, 970 Evans Hall, Berkeley, 94720, USA

    Michele Schiavina

Authors
  1. Alberto S. Cattaneo
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  2. Michele Schiavina
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Corresponding author

Correspondence to Michele Schiavina.

Additional information

Communicated by Krzysztof Gawedzki.

This research was (partly) supported by the NCCR SwissMAP, funded by the Swiss National Science Foundation and by the COST Action MP1405 QSPACE, supported by COST (European Cooperation in Science and Technology). A. S. C. acknowledges partial support of SNF Grant No. 200020_172498\(\slash \)1. M. S. is supported by SNF Grant No. P2ZHP2_164999.

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Cattaneo, A.S., Schiavina, M. The Reduced Phase Space of Palatini–Cartan–Holst Theory. Ann. Henri Poincaré 20, 445–480 (2019). https://doi.org/10.1007/s00023-018-0733-z

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  • DOI: https://doi.org/10.1007/s00023-018-0733-z

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