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arXiv · gr-qc/0612071

Plebanski Theory and Covariant Canonical Formulation

Sergei Alexandrov·Eric Buffenoir·Philippe Roche
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Abstract

We establish an equivalence between the Hamiltonian formulation of the Plebanski action for general relativity and the covariant canonical formulation of the Hilbert-Palatini action. This is done by comparing the symplectic structures of the two theories through the computation of Dirac brackets. We also construct a shifted connection with simplified Dirac brackets, playing an important role in the covariant loop quantization program, in the Plebanski framework. Implications for spin foam models are also discussed.

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Sergei Alexandrov, Eric Buffenoir, Philippe Roche. 2006-12-12. Plebanski Theory and Covariant Canonical Formulation. https://doi.org/10.1088/0264-9381%2F24%2F11%2F003

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