Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 013, 7 pages      quant-ph/0602002      https://doi.org/10.3842/SIGMA.2006.013

Operator Gauge Symmetry in QED

Siamak Khademi a and Sadollah Nasiri a, b
a) Department of Physics, Zanjan University, P.O. Box 313, Zanjan, Iran
b) Institute for Advanced Studies in Basic Sciences, IASBS, Zanjan, Iran

Received October 09, 2005, in final form January 17, 2006; Published online January 30, 2006

Abstract
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.

Key words: gauge transformation; Maxwell's equations; electromagnetic fields.

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