Vol. 39

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues

The Extended Gauge Transformations

By Arbab Ibrahim Arbab
Progress In Electromagnetics Research M, Vol. 39, 107-114, 2014


In this work, new ``extended gauge transformations'' involving current and fields are presented. The transformation of Maxwell's equations under these gauges leads to a massive boson field (photon) that is equivalent to Proca field. The charge conservation equation and Proca equations are invariant under the new extended gauge transformations. Maxwell's equations formulated with Lorenz gauge condition violated give rise to massive vector boson. The inclusion of London supercurrent in Maxwell's equations yields a massive scalar boson satisfying Klein-Gordon equation. It is found that in superconductivity Lorenz gauge condition is violated, and consequently massive spin-0 bosons are created. However, the charge conservation is restored when the total current and charge densities are considered.


Arbab Ibrahim Arbab, "The Extended Gauge Transformations," Progress In Electromagnetics Research M, Vol. 39, 107-114, 2014.


    1. Arbab, A. I., "The analogy between matter and electromagnetic waves," Europhysics Letters, Vol. 94, No. 5, 50005, 2011.

    2. Vigier, J. P., "Evidence for nonzero mass photons associated with a vacuum-induced dissipative red-shift mechanism," IEEE Transactions on Plasma Science, Vol. 18, No. 1, 64-72, 1990.

    3. Kar, G., M. Sinha, and S. Roy, "Maxwell equations, nonzero photon mass, and conformal metric fluctuation," Int. J. Theor. Phys., Vol. 32, 593-607, 1993.

    4. Bardeen, J., L. N. Cooper, and J. R. Schrieffer, "Theory of superconductivity," Phys. Rev., Vol. 108, 1175, 1957.

    5. Bass, L. and E. Schodinger, "Must the photon mass be zero?," Proc. Roy. Soc. London A, Vol. 232, No. 1188, 1-6, 1955.

    6. Proca, A., "Sur la theorie ondulatoire des electrons positifs et negatifs," J. Phys. Radium, Vol. 7, 347-353, 1936.

    7. Aharonov, Y. and D. Bohm, "Significance of electromagnetic potentials in the quantum theory," Phys. Rev., Vol. 115, 485, 1959.

    8. Higgs, P. W., "Broken symmetries and the masses of gauge bosons," Phys. Rev. Lett., Vol. 13, 508, 1964.

    9. Ginzburg, V. L. and L. D. Landau, "On the theory of superconductivity," Zh. Eksp. Teor. Fiz., Vol. 20, 1064-1082, 1950.

    10. Tu, L.-C., J. Luo, and G. T. Gilles, "The mass of the photon," Rep. Prog. Phys., Vol. 68, 77, 2005.

    11. Lakes, R., "Experimental limits on the photon mass and cosmic magnetic vector potential," Phys. Rev. Lett., Vol. 80, 1826, 1998.

    12. Goldhaber, A. S. and M. M. Nieto, "Terrestrial and extraterrestrial limits on the photon mass," Rev. Mod. Phys., Vol. 43, 277, 1971.

    13. Poenaru, D. N. and A. Calboreanu, Europhysics News, Vol. 37, 24, 1990.

    14. Van Vlaenderen, K. J., "generalization of classical electrodynamics for the prediction of scalar field effects," Classical Physics, 2003, http://arxiv.org/abs/physics/0305098v1.

    15. Griffiths, D., Introduction to Electrodynamics, Prentice-Hall, 1999.

    16. Arbab, A. I. and Z. A. Satti, "The generalized Maxwell equations and the prediction of electroscalar wave," Progress in Physics, Vol. 2, 8, 2009.

    17. Arbab, A. I. and H. M. Widatalla, "The generalized continuity equation," Chinese Physics Letters, Vol. 27, 084703, 2010.

    18. Arbab, A. I., "Complex Maxwell's equations," Chin. Phys. B, Vol. 22, No. 3, 030301, 2013.