Concept of Fully Dually Symmetric Classical and Quantum Electrodynamics

Details Concept of Fully Dually Symmetric Classical and Quantum Electrodynamics Concept of Fully Dually Symmetric Classical and Quantum Electrodynamics

2011-02-13

arxiv.org/abs/1102.2619v2

Physics

Mathematical Physics

23 pages

Scientific paper

It has been shown, that electromagnetic field (EM) has in general case quaternion structure, consisting of four independent fields, which differ each other by the parities under space inversion and time reversal. It has also been shown, that for any complex relativistic field the gauge invariant conserving quantity is two-component scalar or pseudoscalar value - \textit{complex} charge. Generalized Maxwell equations for quaternion four-component EM-field are obtained on the basis of its both dual and hyperbolic dual symmetries. Invariants for EM-field, consisting of dually symmetric parts, for both the cases of dual symmetry are found. It is shown, that the only one physical conserving quantity corresponds to both dual and hyperbolic dual symmetry of Maxwell equations. It is spin in general case and spirality in the geometry, when vector $\vec{E}$ is directed along absciss axis, $\vec{H}$ is directed along ordinate axis in $(\vec{E}, \vec{H})$ functional space. In fact it is the proof for quaternion four component structure of EM-field to be a single whole, that is confirmation along with the possibility of the representation of EM-field in four component quaternion form the necessity of given representation. It extends the overview on the nature of EM-field itself. Canonical Dirac quantization method is developed in two aspects. The first aspect is the application of Dirac quantization method the only to observable quantities. The second aspect is the realization along with well known time-local quantization of space-local quantization and space-time-local quantization. It is shown, that Coulomb field can be quantized in 1D and 2D systems, that is it is radiation field in given low-dimensional systems.

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