Invariances of approximately relativistic Hamiltonians and the center-of- mass theorem
In an earlier paper we considered a class of Lagrangians for directly interacting particles, arising from a slow-motion approximation in various special- and general-relativistic field theories. It was shown that, if the Lagrangian is invariant under time and space translations, this implies invariance under an additional three-parameter set of infinitesimal transformations, which leads directly to the center-of-mass theorem. This result is rederived here in a Hamiltonian formalism, in which these infinitesimal transformations are shown to be generators of a Lie symmetry group in phase space. Then we consider the problem of the most general form possible of a canonical post-Newtonian theory, that is a realization of the Lie algebra of the Poincare group to order c$sup -2$ and that arises from a theory of the usual Newtonian type with two-body interactions. It is found that in such a theory the world- line condition is satisfied to order c$sup -2$. This canonical theory encompasses all the approximately relativistic interactions, found recently by Woodcock and Havas, which follow from a Fokker-type special-relativistic variational principle for particles with direct two-body interactions. The relation of our work to various other approaches to approximately relativistic theories of interacting particles is discussed. (AIP)
- Research Organization:
- Department of Physics, Boston University, Boston, Massachusetts 02215
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-33-031396
- OSTI ID:
- 4016964
- Journal Information:
- Phys. Rev., D, v. 13, no. 6, pp. 1598-1613, Journal Name: Phys. Rev., D, v. 13, no. 6, pp. 1598-1613; ISSN PRVDA
- Country of Publication:
- United States
- Language:
- English
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