2006/12/12 by Sergey Alexandrov, Sergei Alexandrov, E. Buffenoir +3 · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Canonical quantization #Classical mechanics #Cosmology and Gravitation Theories #Covariant Hamiltonian field theory #Covariant transformation #Equivalence (formal languages) #General relativity #Hamiltonian (control theory) #Hamiltonian system #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Symplectic geometry #Theoretical physics #gr-qc
paper · pdf · doi:10.1088/0264-9381/24/11/003
published as Class.Quant.Grav.24:2809-2824,2007 · 18 pages
arxiv created 2006/12/12 · openalex publication_date 2007/05/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 programme, in the Plebanski framework. Implications for spin foam models are also discussed.