Symmetries of the relativistic two-particle model with scalar-vector interaction. (English) Zbl 0952.35148
A relativistic two-particle model with superposition of time-asymmetric scalar and vector interactions is proposed and its symmetries are considered. It is shown that the first integrals of motion satisfy nonlinear Poisson bracket relations which include the Poincaré algebra and one of the algebras \(so(1,3)\), \(so(4)\) or \(e(3)\). Moreover, it is shown how to obtain the relative and particle trajectories using the Runge-Lentz vector instead integrating the equations of motion.
Reviewer: G. A. Bugaenko (Cherkassy)
MSC:
| 35Q75 | PDEs in connection with relativity and gravitational theory |
| 35Q40 | PDEs in connection with quantum mechanics |
| 83C10 | Equations of motion in general relativity and gravitational theory |
Keywords:
relativistic two-particle modelReferences:
| [1] | Droz-Vincent, P.; Nurkowski, P., Symmetries in predictive relativistic mechanics, J. Math. Phys., 31, 10, 2393-2398, 1990 · Zbl 0734.70015 |
| [2] | Duviryak A. and Tretyak V., Classical relativistic dynamics of two bodies on light cone, Cond. Mat. Phys., 1993, N 1, 92-107 (in Ukr.). |
| [3] | Duviryak A., Prepr. ICMP-94-14U, Lviv, 1994 (in Ukr.). |
| [4] | Duviryak A., Tretyak V. and Shpytko V., Exactly solvable two-particle models in the isotropic form of relativistic dynamics, in Proceedings of the Workshop on Soft Physics “Hadrons-94”, Editors G. Bugrij, L. Jenkovszky and E. Martynov, Kiev, 1994, 353-362. |
| [5] | Havas P., Galilei- and Lorentz-invariant particle systems and their conservation laws, Problems in the Foundations of Physics, Springer, Berlin, 1971, 31-48. |
| [6] | Bakamjian, B.; Thomas, LH, Relativistic particle dynamics.II, Phys. Rev., 92, 5, 1300-1310, 1953 · Zbl 0052.22301 |
| [7] | Staruszkiewicz, A., Canonical theory of the two-body problem in the classical relativistic electrodynamics, Ann. Inst. H. Poincaré, 14, 1, 69-77, 1971 |
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