Mathematical differences and physical similarities between Eliezer-Ford-O'connell equation and Landau-Lifshitz equation
J.F. García-Camachoa, E. Salinasb, A. Avalos-Vargasa and G. Ares de Pargaa
a Dpto. de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, U.P. Adolfo López Mateos, Zacatenco, 07738, México D.F., México. e-mail: gadpau@hotmail.com
b Escuela Superior de Computo, Instituto Politécnico Nacional, Av. Miguel Othón de Mendizábal s/n. Col. La Escalera. C.P. 07738, México D.F., México.
]]> Received 17 March 2015.
Abstract
Recently, for high intensity electromagnetic waves, it has been proven that the solutions for the Eliezer-Ford-O'Connell equation and the Landau-Lifshitz equation coincide within a physically detectable range. For large-scale temporal effects, similar results are obtained for the central force problem. However, in the case of a constant magnetic field, the frequencies which describe the motion in both equations differ. Nonetheless, quantum constraints avoid the measurement of such difference making both equations physically equivalent for all the scale of energies and fields within Classical Mechanics regime.
Keywords: Reaction force; classical electrodynamics; special relativity.
PACS: 03.30.+p; 03.50.-z; 03.50.De; 11.10.-z
DESCARGAR ARTÍCULO EN FORMATO PDF
]]> References
1. R. T. Hammond, EJTP 7 (2010) 221. [ Links ]
2. R. T. Hammond, Phys. Rev. A 81 (2010) 062104. [ Links ]
3. R. T. Hammond, Adv. Studies Theor. Phys. 5 (2011) 275. [ Links ]
4. R. T. Hammond, arXiv:0902.4231v2 [physics.class-ph] 21 Jul 2009. [ Links ]
5. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, 2nd ed. (Pergamon, London, 1962) 76. [ Links ]
6. H. Spohn, Europhys. Lett. 50 (2000) 287. [ Links ]
7. F. Rohrlich, Am. J. Phys. 68 (2000) 1109. [ Links ]
8. F. Rohrlich, Phys. Lett. A 283 (2001) 276. [ Links ]
9. G. Ares de Parga, Found. Phys. 36 (2006) 1474. [ Links ] 10. R. Medina, J. Phys. A 39 (2006) 3801. [ Links ]
]]>11 . F. Rohrlich, Classical Charged Particles, Supplement (World Scientific, New Jersey, 2007) p. 257. [ Links ]
12. D. J. Griffiths, T. C. Proctor, D. F. Schroeter, Am. J. Phys. 78 (2010) 391. [ Links ]
13. A. Di Piazza, C. Müller, K. Z. Hatsagortsyan, C. H. Keitel, Rev. Mod. Phys. 84 (2012) 1177. [ Links ]
14. C. S. Shen, Phys. Rev. D 6 (1972) 2736. [ Links ]
15. S. G. Rajeev, Ann. Phys. 323 (2008) 2654. [ Links ]
]]>16. G. W. Ford, R. F. O'Connell, Phys. Lett. A 157 (1991) 217. [ Links ]
17. G. W. Ford, R. F. O'Connell, Phys. Lett. A 174 (1993) 182. [ Links ]
18. C. J. Eliezer, Proc. Roy. Lond. A 194 (1948) 543. [ Links ]
19. S. Parrot, Relativistic Electrodynamics and Differential Geometry (Springer-Verlag, New York, 1986) Chap. 5. [ Links ]
20. T. C. Mo, C. H. Papas, Phys. Rev. D 4 (1971) 3566. [ Links ]
]]>21. Y. Kravets, A. Noble, D. Jaroszynski, Phys. Rev. E 88 (2013) 011201(R). [ Links ]
22. A. Di Piazza, Lett. Math. Phys. 83 (2008) 305. [ Links ]
23. M. Dehghani, J. of Mod. Phys. 2 (2011) 1415. [ Links ]
24. G. Ares de Parga, Il Nuovo Cimento 114 B (1999) 1179. [ Links ]
25. P. A. M. Dirac, Proc. Roy. Soc. A 167 (1938) 148. [ Links ]
]]>26. H. Spohn, Dynamics of Charged Particles and their Radiation Field (Cambridge University Press, 2004) Chap. 9. [ Links ]
27. G. Ares de Parga, R. Mares, S. Domínguez, Ann. Fond. Louis de Broglie 30 (2005)283. [ Links ]
28. G. Ares de Parga, R. Mares, J. Math. Phys. 40 (1999) 4807. [ Links ]
29. N. A. Krall and A. W. Trivelpiece, Principles of Plasma Physics (McGrawHill, 1973). [ Links ]
30. F. Rohrlich, Classical Charged Particles (Addison, Reading, 1965) Chaps. 5 and 6 . [ Links ]
]]>31. G. Ares de Parga, M. Ortiz-Domínguez, R. Mares, Indian J. Phys. 82 (2008) 927. [ Links ]
32. G. W. Ford, R. F. O'Connell, Phys. Lett. A 158 (1991) 31. [ Links ]
33. F. Camilo et al., The Astrophysical Journal 541 (2000) 367. [ Links ]
34. T. C. Quinn and R. M. Wald, Phys. Rev. D 56 (1997) 3381. [ Links ]
35. J. M. Hobbs, Annals of Physics 47 (1968) 141. [ Links ]
]]>36. M. J. Pfenning and E. Poisson, Phys. Rev. D. 65 (2002) 084001. [ Links ]
]]>