Annales Henri Poincaré

, Volume 20, Issue 2, pp 445–480 | Cite as

The Reduced Phase Space of Palatini–Cartan–Holst Theory

  • Alberto S. Cattaneo
  • Michele SchiavinaEmail author


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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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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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Institut für MathematikZurichSwitzerland
  2. 2.Department of MathematicsUniversity of California, BerkeleyBerkeleyUSA

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