In this paper, operator gauge transformation, first introduced by Kobe, is
applied to Maxwell's equations and continuity equation in QED. The gauge
invariance is satisfied after quantization of electromagnetic fields. Inherent
nonlinearity in Maxwell's equations is obtained as a direct result due to the
nonlinearity of the operator gauge transformations. The operator gauge
invariant Maxwell's equations and corresponding charge conservation are
obtained by defining the generalized derivatives of the first and second kinds.
Conservation laws for the real and virtual charges are obtained too. The
additional terms in the field strength tensor are interpreted as electric and
magnetic polarization of the vacuum.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA