Abstract
In the present article we propose a simple equality involving the Dirac operator and the Maxwell operators under chiral approach. This equality establishes a direct connection between solutions of the two systems and moreover, we show that it is valid when the natural relation between the frequency of the electromagnetic wave and the energy of the Dirac particle is fulfilled if the electric field E is parallel to the magnetic field H. Our analysis is based on the quaternionic form of the Dirac equation and on the quaternionic form of the Maxwell equations. In both cases these reformulations are completely equivalent to the traditional form of the Dirac and Maxwell systems. This theory is a new quantum mechanics (QM) interpretation. The below research proves that the QM represents the electrodynamics of the curvilinear closed chiral waves. It is entirely according to the modern interpretation and explains the particularities and the results of the quantum field theory. Also this work may help to clarify the controversial relation between Maxwell and Dirac equations while presenting an original way to derive the Dirac equation from the chiral electrodynamics, leading, perhaps, to novel conception in interactions between matter and electromagnetic fields. This approach may give a reinterpretation of Majorana equation, neutrino mass, violation of Heinsenberg’s measurement-disturbation relationship and mass generation in systems like graphene devices.
Highlights
In mathematical physics, the relation between the two most important first order systems of partial differential equations, (Dirac equation and Maxwell’s equations), is among those topics which attract attention because of their general significance and solutions of particular problems concerning physical models
Our analysis is based on the quaternionic form of the Dirac equation and on the quaternionic form of the Maxwell equations
We propose to find an equivalence between the Dirac equation and the Beltrami equations in quaternionic coordinates
Summary
The relation between the two most important first order systems of partial differential equations, (Dirac equation and Maxwell’s equations), is among those topics which attract attention because of their general significance and solutions of particular problems concerning physical models. In [13] we find that the author shows that in the formulation of [12], based on spinor form there is no physically meaningful way to transform Maxwell’s and Dirac’s equations into each other This statement is valid for standard Maxwell fields, but not for parallel electromagnetic fields that will be discussed in this paper. We propose to find an equivalence between the Dirac equation and the Beltrami equations in quaternionic coordinates This equality establishes a direct connection between solutions of the two systems and we show that it is valid when a quite natural relation between the frequency of the electromagnetic wave and the energy of the Dirac particle is fulfilled. Under this condition we have no radiation and the vector Poynting E H is zero
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