Classical and Quantum Electrodynamics Concept Based on Maxwell Equations’ Symmetry

Abstract

The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. They are reviewed in the work presented. It is drawing the attention on the following aspects. EM-field has in general case quaternion structure, consisting of four independent field constituents, which differ from each other by the parities under space inversion and time reversal. Any complex relativistic field has the gauge invariant scalar (pseudoscalar) conserving quantity - complex charge. There exists physical conserving quantity, which is simultaneously invariant under both Rainich dual and additional hyperbolic dual symmetry transformation of Maxwell equations. It is spin in general case or spirality in the corresponding geometry. EM-field is described instead of unobservable vector and scalar potentials by observable electric field 4-vector-function with the components  and (or in the case of free EM-field) by means of magnetic field 4-vector-function  where   are the -component of 4-current density, corresponding to contribution of electric and magnetic components of charge densities correspondingly, λ is conductivity, which for the case of EM-field propagation in vacuum is  =   . Generalized Maxwell equations for quaternion four-component EM-field are presented. Invariants for EM-field, consisting of dually symmetric parts are found. The proof of the main postulate of quantum mechanics: "To any mechanical quantity can be set up in the correspondence the Hermitian matrix by quantization" is given. Canonical Dirac quantization method was developed in reviewed works in two aspects. The first aspect is its application 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 was also shown, that Coulomb field can be quantized in 1D and 2D systems. New model of photons was proposed. The photons in quantized linearly polarized EM-field are main excitations in oscillator structure of EM-field, which is equivalent to spin S = 1 "boson-atomic" 1D lattice structure, consisting of the "atoms" with zeroth rest mass. The photons of the first kind and of the second kind represent themselves respectively neutral spin 1/2 EM-solitons and charged spinless EM-solitons of Su-Schrieffer-Heeger family.