The Extended Gauge Transformations

Abstract

In this work, new \extended gauge transformations" involving current and ¯elds are presented. The transformation of Maxwell's equations under these gauges leads to a massive boson ¯eld (photon) that is equivalent to Proca ¯eld. 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.