Department of Physics,

Zanjan University,

PO Box 313,

Zanjan, IRAN

E-mail: Skhademi@mail.znu.ac.ir, Siamakkhademi@yahoo.com, nasiri@iasbs.ac.ir

**Operator gauge symmetries in QED**

**Abstract:**

Symmetry considerations under some specific transformations are fundamental
properties of any dynamical system. These symmetries, ordinarily, lead
to conserved quantities which can principally be measured. For a system
of electric charges an important quantity that is always required to be
conserved is the total charge. The symmetry operation under which the charge
is conserved is known as gauge transformation. Here, the Kobe approach
to QED is extended to obtain an operator gauge invariant form of the Maxwell
equations and the corresponding law of the charge conservation. The notions
of the commutative and the non-commutative gauges are introduced. The conservation
of the real and virtual charges, as a consequence of this notion, is
obtained separately. This technique seems to be applicable to nonlinear
quantum optics and quantizing the Electromagnetic field in a dielectric
meduim.