Abstract
In this paper—dedicated to Prof. Asim O. Barut—we generalize the Diracnon-linear electrodynamics by introducing two potentials(namely, the vector potential A and the pseudo-vector potential γ5B of the electromagnetic theorywith charges and magnetic monopoles) and by imposing the pseudoscalar part of the product ωω* to be zero, with ω≡A+γ5B. We show that the field equations of such a theory possess a soliton-like solution which can representa priori a “charged particle,” since it is endowed with a Coulomb field plus the field of a magneticdipole. The rest energy of the soliton is finite, and the angular momentum stored in its electromagnetic field can be identified—for suitable choices of the parameters—with the spin of the charged particle. Thus, this approach seems to yield a classical model for the charged (spinning) particle which does not encounter the problems met by earlier attempts in the same direction.
Similar content being viewed by others
References
See, e.g., A. O. Barut,Lett. Math. Phys. 10, 195 (1985); A. O. Barut and R. R484-1czka,Lett. Math. Phys. 1, 315 (1976); A. O. Barut and A. Zanghi,Phys. Rev. Lett. 52, 2009 (1984); A. O. Barut and M. Pavšič,Class. Quant. Grav. 4, L131 (1987).
E. Whittaker,A History of the Theories of Theories of Aether and and Electricity, Vol. 1 (Humanities Press, New York, 1973).
F. Rohrlich, “The electron: Development of the first elementary particle theory,” in J. Mehra, ed.,The Physicist's Conception of Nature (Reidel, Dordrecht, 1973), pp. 331–369.
M. Abraham,Ann. Phys. (Leipzig) 10, 105 (1903).
H. A. Lorentz,Theory of Electrons, 2nd edn. (Dover, New York, 1952).
J. D. Jackson,Classical Electrodynamics (Wiley, New York, 1962).
P. A. M. Dirac,Proc. R. Soc. London A 168 (1938).
See, e.g., P. Caldirola,Suppl. Nuovo Cimento 3, 297 (1956).
P. A. M. Dirac,Proc. R. Soc. London A 209 292 (1951);212, 330 (1952);223, 458 (1954).
P. A. M. Dirac,Nature (London) 168, 906 (1951).
Cf. A. Proca,J. Phys. Radium 7, 347 (1936). See also E. Schroedinger,Proc. R. Irish Acad. A 48, 135 (1943).
R. Righi and G. Venturi,Int. J. Theor. Phys. 21, 63 (1982).
W. A. Rodrigues, Jr. and V. L. Figueiredo,Int. J. Theor. Phys. 24, 413 (1990).
W. A. Rodrigues, Jr., E. Recami, A. Maia, Jr., and M. A. F. Rosa,Phys. Lett. B 220, 195 (1989);173, 233 (1986);188, E511 (1987). See also E. Mignani and E. Recami,Nuovo Cimento A30, 533 (1975); E. Recami,Riv. Nuovo Cimento 9, issue No. 6, pages 85, 156 (1986) and references therein.
W. A. Rodrigues, Jr., M. A. Faria-Rosa, A. Maia, Jr., and E. Recami,Hadronic J. 12, 187 (1989).
D. Hestenes,Space-Time Algebra (Gordon & Breach, New York, 196).
M. Riesz,Clifford Numbers and Spinors (Lecture Series No. 38) (Institute for Fluid Mechanics and Applied Mathematics, University of Maryland, 1958).
R. Penrose and W. Rindler,Spinors and Space-Time, Vol. I (Cambridge University Press, Cambridge, 1983).
A. O. Barut,Electrodynamics and Classical Theory of Fields and Particles (Dover, New York, 1980).
N. Cabibbo and E. Ferrari,Nuovo Cimento 23, 1147 (1962).
P. Caldirola, M. Pavšič, and E. Recami,Nuovo Cimento B 48, 205 (1978); E. Recami,Prog. Part. Nucl. Phys. 8, 401 (1982);Found. Phys. 13, 341 (1983); P. Caldirola,Nuovo Cimento A 49, 497 (1979); E. Recami, inOld and New Questions in Physics, Cosmology, Philosophy, and Theoretical Biology, A. van der Merwe, ed. (Plenum, New York, 1982), p. 377.
D. Hestenes,Am. J. Phys. 47, 399 (1979). See also M. Paršič, E. Recami, W. A. Rodrigues Jr., G. D. Maccarrone, F. Raciti, G. Salesi: “Spin and electron structure,” Report INFN/AE-92/27 (Frascati, 1992), submitted for publication.
Author information
Authors and Affiliations
Additional information
Work partially supported by INFN, CNR, MURST and by FUNREI and CNPq.
Rights and permissions
About this article
Cite this article
Rodrigues, W.A., Vaz, J. & Recami, E. A generalization of Dirac nonlinear electrodynamics, and spinning charged particles. Found Phys 23, 469–485 (1993). https://doi.org/10.1007/BF01883725
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01883725