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Article Dans Une Revue Annales Henri Poincaré Année : 2011

Complex Ashtekar variables and reality conditions for Holst's action

Résumé

From the Holst action in terms of complex valued Ashtekar variables additional reality conditions mimicking the linear simplicity constraints of spin foam gravity are found. In quantum theory with the results of You and Rovelli we are able to implement these constraints weakly, that is in the sense of Gupta and Bleuler. The resulting kinematical Hilbert space matches the original one of loop quantum gravity, that is for real valued Ashtekar connection. Our result perfectly fit with recent developments of Rovelli and Speziale concerning Lorentz covariance within spin-form gravity.

Dates et versions

hal-00556665 , version 1 (17-01-2011)

Identifiants

Citer

Wolfgang Wieland. Complex Ashtekar variables and reality conditions for Holst's action. Annales Henri Poincaré, 2011, pp.24. ⟨10.1007/s00023-011-0134-z⟩. ⟨hal-00556665⟩
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