Abstract
We compare, in bothD=3 andD=4, two vielbein canonical formulations of gravity: that of Deser and Isham which starts with the metric replaced by vielbeins in the ADM action, and that starting directly from first order vielbein action, and compute the functional that generates the canonical transformation between these two formulations. InD=3, the generator thus exhibits the inherent simplicity of the Einstein action, starting from the DI form (which is as complicated as inD=4). InD=4, however, the same procedure, while leads to a somewhat different formulation from the existing ones, does not result in miraculous simplifications.
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Xiang, X. Canonical vielbein forms ofD=3 andD=4 gravity. Gen Relat Gravit 25, 1019–1029 (1993). https://doi.org/10.1007/BF00763552
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DOI: https://doi.org/10.1007/BF00763552