Action-at-a-Distance and Radiation Reaction of Point-Like Particles in de Sitter Space
Keywords:Staruszkiewicz–Rudd–Hill model, de Sitter space, electromagnetic self-force
The two-particle system with the time-asymmetric retarded-advanced electromagnetic interaction known as the Staruszkiewicz–Rudd–Hill model is considered in the de Sitter space-time. The manifestly covariant descriptions of the model within the Lagrangian and Hamiltonian formalisms with constraints are proposed. It is shown that the model is de Sitter-invariant and integrable. An explicit solution of the equations of motion is derived. We use the covariant electromagnetic Green function in the de Sitter space in order to derive the equation of motion of a point charge in an external electromagnetic field, where the radiation reaction is taken into account.
A. Staruszkiewicz. An example of a consistent relativistic mechanics of point particles. Ann. Phys. 25, 362 (1970). https://doi.org/10.1002/andp.19704800404
A. Staruszkiewicz. Canonical theory of the two-body problem in the classical relativistic electrodynamics. Ann. I. H. Poincar'e 14, 69 (1971).
R.A. Rudd, R.N. Hill. Exactly solvable electrodynamic two-body problem. J. Math. Phys. 11, 2704 (1970). https://doi.org/10.1063/1.1665436
H. Tetrode. ¨ Uber der wirkungzusammenhang der welt. Eine erweiterung der klassischen dynamik. Z. Phys. 10, 317 (1922). https://doi.org/10.1007/BF01332574
A.D. Fokker. Ein invarianter variationsatz f¨ur die bewegung mehrerer elektrischer massenteilchen. Z. Phys. 28, 386 (1929). https://doi.org/10.1007/BF01340389
H.P. K¨unzle. A relativistic analogue of the Kepler problem. Int. J. Theor. Phys. 11, 395 (1974). https://doi.org/10.1007/BF01809718
A. Duviryak. The two-body time-asymmetric relativistic models with field-type interaction. Gen. Relat. Gravit. 30, 1147 (1998). https://doi.org/10.1023/A:1026638726900
A. Duviryak. Fokker-type confinement models from effective Lagrangian in classical Yang-Mills theory. Int. J. Mod. Phys. A 14, 4519 (1999). https://doi.org/10.1142/S0217751X99002128
A. Duviryak. The two-particle time-asymmetric relativistic model with confinement interaction and quantization. Int. J. Mod. Phys. A 16, 2771 (2001). https://doi.org/10.1142/S0217751X01004360
A. Duviryak, V. Shpytko. Relativistic two-particle mass spectra for time-asymmetric Fokker action. Rep. Math. Phys. 48, 219 (2001). https://doi.org/10.1016/S0034-4877(01)80082-3
F. Hoyle, J.V. Narlikar. Action at a distance in physics and cosmology (Freemen, 1974).
Yu.S. Vladimirov, A.Yu. Turygin, Theory of direct interparticle interaction (' Energoatomizdat, 1986).
H.S.M. Coxeter. A geometrical background for de Sitter's world. Amer. Math. Monthly 50, 217 (1976). https://doi.org/10.2307/2303924
U. Moschella. The de Sitter and anti-de Sitter sightseeing tour. S'eminaire Poincar'e 1, 1 (2005).
A. Higuchi, L.Y. Cheong. How to use retarded Green's functions in de Sitter spacetime. Phys. Rev. D 78, 084031 (2008). https://doi.org/10.1103/PhysRevD.78.084031
J.V. Narlikar. Biscalar and bivector Green's functions in de Sitter space time. Proceedings of the National Academy of Sciences 65, 483 (1970). https://doi.org/10.1073/pnas.65.3.483
P.A.M. Dirac. Generalized Hamiltonian dynamics. Can. J. Math. 2, 129 (1950). https://doi.org/10.4153/CJM-1950-012-1
D.M. Fradkin. Covariant electromagnetic projection operators and a covariant description of charged particle guiding centre motion. J. Phys. A 11, 1069 (jun 1978). https://doi.org/10.1088/0305-4470/11/6/010
E. Poisson, A. Pound, I. Vega. The motion of point particles in curved spacetime. Living Reviews in Relativity 14, 7 (2011). https://doi.org/10.12942/lrr-2011-7
R. Aldrovandi et al. de Sitter Relativity and Quantum Physics. AIP Conf. Proc. 962, 175 (2007). https://doi.org/10.1063/1.2827302
Yu. Yaremko. Self-force via energy-momentum and angular momentum balance equations. J. Math. Phys. 52, 012906 (2011). https://doi.org/10.1063/1.3531986
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