Mathematics – Logic
Scientific paper
Apr 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986gregr..18..411f&link_type=abstract
General Relativity and Gravitation, Volume 18, Issue 4, pp.411-431
Mathematics
Logic
1
Gravitation Theory:Electromagnetic Fields
Scientific paper
It is shown that by solving 12 of the field equations with respect to the connection components hat Γ _0^{(0)(i)} and hat Γ _k^{(a)(b)} , the quantities used to describe the geometry of space-time can be divided into two sets. In the first set we have the canonical variables the time evolution of which is determined by the dynamical equations. The second set contains ten gauge variables N, Nk, tilde Γ _0^{(a)(b)} , n (i) which can be given arbitrarily on space-time. This partial reduction of the Hamiltonian equations enabls us to discuss the initial value problem in the ECSK theory of gravity coupled to matter tensor fields. Such an analysis is performed for the phenomenological ECSK theory and for the ECSK theory coupled to: a covector matter field, the generalized Maxwell electrodynamics, and the generalized Fermi-Dirac electrodynamics. The Poisson brackets of the seven Hamiltonian constraints, which have to be satisfied by the canonical variables, are found. It is proved that they are first class.
Frąckiewicz Kazimierz
Szczyrba Wiktor
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