Abstract
In this paper we present an analysis of the possible equivalence of Dirac and Maxwell equations using the Clifford bundle formalism and compare it with Campolattaro's approach, which uses the traditional tensor calculus and the standard Dirac covariant spinor field. We show that Campolattaro's intricate calculations can be proved in few lines in our formalism. We briefly discuss the implications of our findings for the interpretation of quantum mechanics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barut, A. O. (1990).Physics Letters A,143, 349.
Campolattaro, A. A. (1980a).International Journal of Theoretical Physics,19, 99.
Campolattaro, A. A. (1980b).International Journal of Theoretical Physics,19, 127.
Campolattaro, A. A. (1990).International Journal of Theoretical Physics,29, 141.
Doubrovine, B., Novikov, S., and Fomenko, A. (1987).Géométrie Contemporaine, Méthodes et Applications, Part 1, Mir, Moscow.
Figueiredo, V. L., de Oliveira, E. C., and Rodrigues, W. A., Jr. (1990a).International Journal of Theoretical Physics,29, 371.
Figueiredo, V. L., de Oliveira, E. C., and Rodrigues, W. A., Jr. (1990b).Algebras Groups, and Geometries,7, 153.
Gueret, P., and Vigier, J. P. (1982a).Lettere Nuovo Cimento,35, 256.
Gueret, P., and Vigier, J. P. (1982b).Lettere Nuovo Cimento,35, 260.
Gueret, P., and Vigier, J. P. (1982c).Lettere Nuovo Cimento,38, 125.
Hestenes, D. (1966).Space-Time Algebra, Gordon and Breach, New York.
Hestenes, D. (1967).Journal of Mathematical Physics,8, 789.
Hestenes, D. (1975).Journal of Mathematical Physics,16, 556.
Hestenes, D. (1991).Foundations of Physics,20, 1213.
Jennison, R. C. (1978).Journal of Physics A,11, 1525.
Mackinnon, L. (1978).Foundations of Physics,8, 157.
Mackinnon, L. (1981).Lettere Nuovo Cimento,32, 311.
Maia, A., Jr., Recami, E., Rosa, M. A. F., and Rodrigues, W. A., Jr. (1990).Journal of Mathematical Physics,31, 502.
Misner, C. W., and Wheeler, J. A. (1957).Annals of Physics,2, 525.
Rainich, G. Y. (1925).Transactions of the American Mathematical Society,27, 106.
Riesz, M. (1958). Clifford Number and Spinors, Lecture Series No. 38, Institute for Fluid Mechanics and Applied Mathematics, University of Maryland.
Rodrigues, W. A., Jr., and de Oliveira, E. C. (1990).International Journal of Theoretical Physics,29, 397.
Rodrigues, W. A., Jr., Faria-Rosa, M. A., Maia, A., Jr., and Recami, E. (1989).Hadronic Journal,12, 187.
Rodrigues, W. A., Jr., and Figueiredo, V. L. (1990).International Journal of Theoretical Physics,29, 413.
Rodrigues, W. A., Jr., and Vaz, J., Jr. (1992). Nondispersive de Broglie wavepackets from the free Maxwell equations, submitted.
Vaz, J., Jr., and Rodrigues, W. A., Jr. (1992). Particle and antiparticle configurations of the free Maxwell equations satisfying the Dirac equation, submitted.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vaz, J., Rodrigues, W.A. Equivalence of Dirac and Maxwell equations and quantum mechanics. Int J Theor Phys 32, 945–959 (1993). https://doi.org/10.1007/BF01215301
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01215301