Related papers: A new nonlinear generalization of the Dirac equati…
We describe a class of theories of dielectric polarization and a species of solitons in these theories. The solitons, made entirely out of the polarization field, have quantized values of the electric charge and can be interpreted as…
We obtain by invariance arguments the relativistic and non-relativistic invariant dynamical equations of a classical model of a spinning electron. We apply the formalism to a particular classical model which satisfies Dirac's equation when…
As a continuation of previous investigations, the formalism used there is extended to the case when an external electric field is present and the covariant formulation is performed again. The equation system obtained allows no restriction…
We first study the linear eigenvalue problem for a planar Dirac system in the open half-line and describe the nodal properties of its solution by means of the rotation number. We then give a global bifurcation result for a planar nonlinear…
Generalizations of the three main equations of quantum physics, namely, the Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index $q$, are considered in such a way…
Dirac's quantization of the Maxwell theory on non-commutative spaces has been considered. First class constraints were found which are the same as in classical electrodynamics. The gauge covariant quantization of the non-linear equations of…
This paper uses elementary techniques drawn from renormalization theory to derive the Lorentz-Dirac equation for the relativistic classical electron from the Maxwell-Lorentz equations for a classical charged particle coupled to the…
In our Comment we question the validity of the claim made by the authors of \cite{cc} that their solutions of the Dirac equation in an external {\em time-dependent} electromagnetic field describe beams of electrons. In every time-dependent…
The author argues that the Dirac quantization condition might imply the existence of an undiscovered electromagnetic structure which governs the quantization of the electric charge and the quantization of the magnetic flux in the…
Simple arguments based on uncertainty principle and Dirac's equation are examined which show that electron behaves either as a point-like charge or as an extended distribution according as high- or low-energy experiments are considered.
We construct the most general form of our previously proposed nonlinear extension of quantum mechanics that possesses three basic properties. Unlike the simpler model, the new version is not completely integrable, but it has an underlying…
This paper presents new analytic solutions to the Dirac equation employing a recently introduced method that is based on the formulation of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. A first…
We derive a new generalization of the nonlinear variational wave equation. We prove existence of local, smooth solutions for this system. As a limiting case, we recover the nonlinear variational wave equation.
In the first part of the paper we give a tensor version of the Dirac equation. In the second part we formulate and analyse a simple model equation which for weak external fields appears to have properties similar to those of the…
In this paper, we investigate the nonrelativistic limit of normalized solutions to a nonlinear Dirac equation as given below: \begin{equation*} \begin{cases} &-i c\sum\limits_{k=1}^3\alpha_k\partial_k u +mc^2 \beta {u}- \Gamma * (K…
We consider the behavior of the particles at ultra relativistic energies, for both the Klein-Gordon and Dirac equations. We observe that the usual description is valid for energies such that we are outside the particle's Compton wavelength.…
We present some results obtained in collaboration with prof. Piero D'Ancona concerning global existence for the 3D cubic non linear massless Dirac equation with a potential for small initial data in $H^1$ with slight additional assumptions.…
The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong…
The family of solutions to the Dirac equation for an electron moving in an electromagnetic lattice with the chiral structure created by counterpropagating circularly polarized plane electromagnetic waves is obtained. At any nonzero…
We present an approach to compute the electric and magnetic dipole moments of an electron by using polarization and magnetization parts of the Dirac current. We show that these dipole moment expressions obtained by our approach in this…