Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1995-06-05
Nuovo Cim.B110:1137-1152,1995
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
22 pages, plain Tex, no figures, accepted for publication in Nuovo Cimento B
Scientific paper
10.1007/BF02724605
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.
Esposito Giampiero
Gionti Gabriele
Stornaiolo Cosimo
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