Plebanski Theory and Covariant Canonical Formulation

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.

18 pages

References in corpus (1)

• Towards a Covariant Loop Quantum Gravity

Cited by in corpus (4)

• Spin foam model from canonical quantization
• Simplicity and closure constraints in spin foam models of gravity
• Hamiltonian Analysis of non-chiral Plebanski Theory and its Generalizations
• Diffeomorphism symmetry in quantum gravity models