1995/06/05 by Giampiero Esposito, G. Esposito, Gabriele Gionti +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Black Holes and Theoretical Physics #Classical mechanics #Constraint algebra #Cosmology and Gravitation Theories #Covariant Hamiltonian field theory #Covariant transformation #Field equation #Formalism (music) #General relativity #Hamiltonian (control theory) #Hamiltonian constraint #Hamiltonian system #Hypersurface #Lagrangian #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum gravity #Quantum mechanics #Spacetime #Wheeler–DeWitt equation #gr-qc
paper · pdf · doi:10.1007/bf02724605
published as Nuovo Cim.B110:1137-1152,1995 · 22 pages, plain Tex, no figures, accepted for publication in Nuovo Cimento B
arxiv created 1995/06/05 · openalex publication_date 1995/10/01 · arxiv updated 2010/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Lagrangian formulation of classical field theories and in particular general relativity leads to a coordinate-free, fully covariant analysis of these constrained systems. This paper applies multisymplectic techniques to obtain the analysis of Palatini and self-dual gravity theories as constrained systems, which have been studied so far in the Hamiltonian formalism. The constraint equations are derived while paying attention to boundary terms, and the Hamiltonian constraint turns out to be linear in the multimomenta. The equivalence with Ashtekar's formalism is also established. The whole constraint analysis, however, remains covariant in that the multimomentum map is evaluated on \it any spacelike hypersurface. This study is motivated by the non-perturbative quantization program of general relativity.