Zitterbewegung And The Electromagnetic Field Of The Electron

By using the spacetime algebra, we explain the helical motion of the electron (zitterbewegung) and its Coulomb field by introducing a mechanism that breaks locally the electromagnetic gauge invariance. We show that this gauge invariance is broken in all points of spacetime, except for those that correspond to that cylindrical helix which is the electron's world line, and that it gives rise to an oscillating Coulomb-like field with frequency equal to the zitterbewegung one. This field is found to satisfy the so-called Maxwell-London equations. This oscillating field, when averaged over a zitterbewegung period, is the usual Coulomb field of the electron. © 1993.31901/03/15203208Bohr, ON THE NOTIONS OF CAUSALITY AND COMPLEMENTARITY1 (1948) Dialectica, 34, p. 312Hestenes, (1966) Space time algebra, , See, for example, Gordon and Breach, New YorkHestenes, Sobczyk, (1984) Clifford algebra to geometric calculus, , Reidel, DordrechtHestenes, (1967) J. Math. Phys., 8, p. 798Hestenes, (1990) Found. Phys., 20, p. 1213Hestenes, Zitterbewegung in radiative processes (1991) The electron, p. 21. , D. Hestenes, A. Weingartshofer, Kluwer Academic, DordrechtRodrigues, Jr., Vaz, Jr., Recami, (1993) Phys. Lett. B, 318, p. 623Pavšič, Recami, Rodrigues, Jr., Maccarrone, Raciti, Salesi, Spin and electron structure (1993) Physics Letters B, 318, p. 481Reitz, Milford, Christy, (1960) Foundations of electromagnetic theory, , Addison-Wesley, Reading, MALounesto, Clifford algebras and Hestenes spinors (1993) Found. Phys., , Helsinki University of technology preprint (1992), to appearBarut, Bracken, (1981) Phys. Rev. D, 23, p. 2454Figueiredo, de Oliveira, Rodrigues, Jr., (1990) Int. J. Theor. Phys., 29, p. 371. , See, for exampleRodrigues, Jr., Oliveira, (1990) Int. J. Theor. Phys., 29, p. 397Vaz, Jr., Rodrigues, Jr., On the equivalence of Maxwell and Dirac equations, and quantum mechanics (1993) Int. J. Theor. Phys., , to appearRodrigues, Jr., Vaz, Jr., Recami, Free Maxwell equations, Dirac equation and non-dispersive de Broglie wave packets (1992) Courants, amers, écueils en microphysics, , G. Lochak, P. Lochak, Volume in honour of the centennial of Louis de Broglie, Foundation Lous de Broglie, to appearBoudet, (1971) C.R. Acad. Sc. Paris, 292, p. 767Barut, Zanghi, (1984) Phys. Rev. Lett., 52, p. 2009Hestenes, (1985) Found. Phys., 15, p. 63Dirac, A New Classical Theory of Electrons (1951) Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 209, p. 292Dirac, A New Classical Theory of Electrons. II (1952) Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 212, p. 330Dirac, A New Classical Theory of Electrons. III (1954) Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 223, p. 458Rodrigues, Jr., Vaz, Jr., Recami, (1993) Found. Phys., 23, p. 469Ross, Planck's constant, torsion, and space-time defects (1989) International Journal of Theoretical Physics, 28, p. 1933Magnon, (1991) J. Math. Phys., 32, p. 928Gliozzi, (1978) Nucl. Phys. B, 141, p. 37