Classical and Quantum Electrodynamics Concept Based on Maxwell Equations' Symmetry

TL;DR

This paper explores the symmetry properties of Maxwell equations, revealing a quaternion structure of the electromagnetic field, and develops a new photon model based on these symmetries and quantization methods.

Contribution

It introduces a quaternion-based structure of EM fields, derives generalized Maxwell equations, and proposes a novel photon model with soliton-like excitations.

Findings

Quaternion structure of EM field confirmed

Existence of conserved quantities invariant under dual symmetries

New photon model with soliton excitations

Abstract

The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. It has in general case quaternion single structure, consisting of four independent field constituents, which differ with each other by the parities under space inversion and time reversal. Generalized Maxwell equations for quaternion four-component EM-field are obtained. Invariants for EM-field, consisting of dually symmetric parts are found. It is shown, that 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 and spirality in the geometry, when electrical and magnetic vectors $\vec{E}$, $\vec{H}$ are directed along coordinate axes in ($\vec{E}$, $\vec{H}$) functional space. It is additional proof for quaternion four component structure of EM-field to be a single whole. Canonical Dirac quantization method is developed 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 is also shown, that Coulomb field can be quantized in 1D and 2D systems. New model of photons is proposed. The photons in quantized EM-field are main excitations in oscillator structure of EM-field, which is equivalent to spin S = 1 "boson-atomic" structure, like matematically to well known spin S = 1 boson matter structure - carbon atomic backbone chain structure in many conjugated polymers. They have two kind nature. The photons of the first kind and the second kind represent themselves respectively neutral chargeless EM-solitons and charged spinless EM-solitons of Su-Schrieffer-Heeger family.