Abstract
The construction of a formalism for the description of the dynamical properties of many-body systems which is consistent with special relativity, in the framework of classical or quantum theory, is still far from complete. Dime’s proposal,1 in 1949, of Hamiltonian-type theories, developed2,3 into an action-at-a-distance theory with the Lorentz group canonically represented. Currie, Jordan, and Sudarshan,4 however, showed that when the canonical coordinates are taken as the physical coordinates of point particles and their world lines are Lorentz invariant, the only possible dynamics is that of free particles. The history of these developments, and an invaluable collection of reprinted papers, has been provided by Kerner.4 Rohrlich and King5,6 have developed a Hamiltonian theory in which constraint equations control the masses of individual particles and also have the role of generating the evolution of the system.7 For N-body systems, the requirements of compatibility imply the existence of N-body forces (corresponding to the potential functions appearing in the constraint equations).
Research supported in part by the U.S.-Israel Binational Science Foundation (BSF), Jerusalem, Israel
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References and Notes
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I wish to thank Fritz Rohrlich for clarifying this connection.
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© 1983 Plenum Press, New York
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Horwitz, L.P. (1983). On Relativistic Quantum Theory. In: van der Merwe, A. (eds) Old and New Questions in Physics, Cosmology, Philosophy, and Theoretical Biology. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-8830-2_13
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