TITLE:
Chiral Dirac Equation Derived From Quaternionic Maxwell’s Systems
AUTHORS:
Hector Torres-Silva
KEYWORDS:
Quaternion; Dirac Equation; Maxwell System
JOURNAL NAME:
Journal of Electromagnetic Analysis and Applications,
Vol.5 No.3,
March
28,
2013
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.