Plebanski Theory and Covariant Canonical Formulation

Details Plebanski Theory and Covariant Canonical Formulation Plebanski Theory and Covariant Canonical Formulation

2006-12-12

arxiv.org/abs/gr-qc/0612071v1

Class.Quant.Grav.24:2809-2824,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages

Scientific paper

10.1088/0264-9381/24/11/003

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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