Abstract
This work clarifies the relation between Maxwell, Dirac and Majorana neutrino equations presenting an original way to derive the Dirac and neutrino equation from the chiral electrodynamics leading, perhaps, to novel conception in the mass generation by electromagnetic fields. In the present article, it is shown that Maxwell equations can be written in the same form as the two components Dirac and neutrino equations, that is the vector representation of electromagnetic theory can be factorized into a pair of two-component spinor field equations. We propose a simple approach with the electric field E parallel to the magnetic field H. Our analysis is based on the chiral or Weyl form of the Maxwell equations in a chiral vacuum. This theory is a new quantum mechanics (QM) interpretation for Dirac and neutrino equation. The below research proves that the QM of particles represents the electrodynamics of the curvilinear closed chiral waves. Electromagnetic properties of neutrinos are discussed.
Highlights
Maxwell’s equations can be formulated in a number of diferent spinor representations: a) as a single four-component spinor equation whose transformation properties are almost identical with those of the Dirac equation; b) as a pair of uncoupled two-component spinor equations, in two different representations
It is shown that Maxwell equations can be written in the same form as the two components Dirac and neutrino equations, that is the vector representation of electromagnetic theory can be factorized into a pair of two-component spinor field equations
We propose a simple approach with the electric field E parallel to the magnetic field H
Summary
Maxwell’s equations can be formulated in a number of diferent spinor representations: a) as a single four-component spinor equation whose transformation properties are almost identical with those of the Dirac equation; b) as a pair of uncoupled two-component spinor equations, in two different representations. The electromagnetism can be discussed via chiral differential forms, we point out the optical activity of a given material medium, closely related to topological spin, and the Faraday rotation, associated to topological torsion. Both quantities are defined in terms of the chiral magnetic and electric field. The aim of this work is to construct the Dirac equation and the neutrino equation in the Weyl representation through Maxwell’s equations in the chiral formulation This possibility occurs only when the E field and H field are spatially parallel and the field distribution can generate mass.
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