Abstract
In the present paper we determine the properties of classical electron within classical electrodynamics after the “gauge renormalization.” It is shown that a description of the classical electron can be done at the scale less than the classical radius of the electron.
Similar content being viewed by others
References
1. H.A. Lorentz, The Theory of Electrons, 2nd edn. (Dover, New York, 1952).
2. M. Abraham, “Die Prinzipien der Dynamik des Elektrons,” Ann. Phys. 10, 105 (1903).
3. P.A.M. Dirac, “Classical theory of radiating electrons,” Proc. Roy. Soc. (London) A167, 148 (1938).
4. M. Born and L. Infeld, “Foundations of the new field theory,” Proc. Roy. Soc. (London) A 144 145 (1934).
5. E. Rohrlich, Classical Charged Particles (Addison-Wesley, Reading, MA, 1965).
6. L.D. Landau and E.M. Lifshitz, The Classical Theory of Fields, 2nd edn. (Pergamon, New York, 1962).
7. J.D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
8. W.K.H. Panofsky and M. Phillips, Classical Electricity and Magnetisms, 2nd edn. (Addison-Wesley, Reading, MA, 1962).
9. D. Ivanenko and A. Sokolov, Classical Theory of Field (New Problems), 2nd edn. (Gosudarstvennoe Isdatel'stvo Nauchno-Technicheskoj Literatury, Moscow, Leningrad, 1951) (in Russian).
10. A.L. Kholmetskii, “On ‘gauge renormalization’ in classical electrodynamics,” Found. Phys. 35, 715 (2006).
11. H. Poincaré, Rend. Circ. Mat. Palermo 21, 129 (1906). English translation with modern notation in H.M. Schwartz, “Poincaré's Rendincoti paper on relativity,” Am J. Phys. 40, 862 (1972)).
12. K.-II. Yang, “Gauge transformations and quantum mechanics II. Physical interpretation of classical gauge transformations,” Ann. Phys. 101, 97 (1976).
13. G.J.N. Brown, D.S.F Crothers, “Generalized gauge invariance of electromagnetism,” J. Phys. A. 22, 2939 (1989).
14. R.P. Feynman, R.B. Leighton, and M. Sands, The Feynman Lectures in Physics, Vol. 2 (Addison-Wesley, Reading, MA, 1964).
15. J.D. Jackson, “From Lorentz to Coulomb and other explicit gauge transformations,” Am. J. Phys. 70, 917 (2002).
16. A.E. Chubykalo and V.V. Onoochin, “On the theoretical possibility of the electromagnetic scalar potential wave spreading with an arbitrary velocity in vacuum,” Hadronic J. 25, 597 (2002).
17. A. Chubykalo, A. Espinoza, R. Flores-Alvarado, and A. Gutierrez Rodriguez, “Helmholtz theorem and the v-gauge in the problem of superluminal and instantaneous signals in classical electrodynamics,” Found. Phys. Lett. 19, 37 (2006).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kholmetskii, A. Gauge Renormalization in Classical Electrodynamics: Phenomenological Description of the Classical Electron. Found Phys Lett 19, 695–708 (2006). https://doi.org/10.1007/s10702-006-1058-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10702-006-1058-8