Computer Science
Scientific paper
Aug 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982gregr..14..731b&link_type=abstract
General Relativity and Gravitation, Volume 14, Issue 8, pp.731-740
Computer Science
1
Scientific paper
The dynamics of a system of relativistically interacting particles is determined by a set of constraints, some combination of which has been frequently identified with the Hamiltonian. These constraints differ from the generators of the Poincaré transformations, among whichp 0 generates translations along the time axis and hence is to be considered as the energy of the system. There are thus grounds for consideringP 0 as the appropriate Hamiltonian. In this paper we establish a close relationship between transformations generated by the constraints and those generated by the Poincaré generators. In particular we find that the true Hamiltonian is a rather complicated but well-defined function ofp 0 and all the constraints. We show that the generators of the entire algebra of the Poincaré group can be realized in such a fashion that the Hamiltonian is correctly included among them, and such that particle world lines in Minkowski space-time generated by this Hamiltonian transform correctly under the Poincaré group.
Bergmann Peter G.
Komar Arthur
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