Dark states and vortex solutions with finite energy in Maxwell-Dirac nonlinear equations

TL;DR

This paper derives nonlinear Maxwell-Dirac equations from Maxwell's equations in media, finds solitary wave solutions with half-integer spin and finite energy, called dark states, which are electromagnetic waves with unique properties.

Contribution

It introduces a novel derivation of nonlinear Maxwell-Dirac equations and identifies dark state solutions with specific electromagnetic characteristics.

Findings

Found solitary solutions with half-integer spin and finite energy.

Identified dark states as electromagnetic waves with zero divergence.

Described localized energy as electromagnetic mass.

Abstract

Starting from Maxwell equations for media with no-stationary linear and nonlinear polarization, we obtain a set of nonlinear Maxwell amplitude equations in approximation of first order of the dispersion. After a special kind of complex presentation, the set of amplitude equations was written as a set of nonlinear Dirac equations. For broad-band pulses solitary solutions with half-integer spin and finite energy are found. The solutions correspond to electromagnetic wave with circular Poynting vector and zero divergence. These invisible for detectors waves are called dark states and the localized energy we determine as electromagnetic mass.