Related papers: A new nonlinear generalization of the Dirac equati…
In the present paper it is shown that the Dirac electron theory is the approximation of the special nonlinear electromagnetic field theory
We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincar\'e invariance. We determine the constraints…
The recent literature shows a renewed interest, with various independent approaches, in the classical theories for spin. Considering the possible interest of those results, at least for the electron case, we purpose in this paper to explore…
We suggest a tensor equation on Riemannian manifolds which can be considered as a generalization of the Dirac equation for the electron. The tetrad formalism is not used. Also we suggest a new form of the tensor Dirac equation with a…
Dirac's equation of the electron will be discussed by using quaternions as the basis of a new formalism which seems to be very well adapted to the problem. The transformation properties of the equations as well as the invariant and…
The Dirac equation with the Coulomb potential is studied. It is shown that there exists a new invariant in addition to the known Dirac and Johnson-Lippman ones. The solution of the Dirac equation, using the generalized invariant, and…
We discuss a connection between the Dirac equation for an electron and the Dirac type tensor equation with ${\rm U}(1)$ gauge symmetry.
We re-examine the non Hermitian position coordinate of Dirac's equation, in the light of his own insights and conclude that this, and the Dirac equation itself is symptomatic of an underlying Noncommutative Geometry.
Nonlinear generalization of the Dirac equation extending the standard paradigm of nonlinear Hamiltonians is discussed. ``Faster-than-light telegraphs" are absent for all theories formulated within the new framework. A new metric for…
We show that the Dirac theory of the electron, corresponds to recent approaches based on a Non commutative spacetime.
A novel interpretation is given of Dirac's "wave equation for the relativistic electron" as a quantum-mechanical one-particle equation. In this interpretation the electron and the positron are merely the two different "topological spin"…
The nilpotent Dirac formalism has been shown, in previous publications, to generate new physical explanations for aspects of particle physics, with the additional possibility of calculating some of the parameters involved in the Standard…
A general relation is derived between the linear and second-order nonlinear ac conductivities of an electron system in the hydrodynamic regime of frequencies below the interparticle scattering rate. The magnitude and tensorial structure of…
The present paper is the continuation of the paper "Nonlinear field theory I". In the paper it is shown that a fully correspondence between the quantum and the nonlinear electromagnetic forms of the Dirac electron theory exists, so that…
We derive the modified Dirac equation for an electron undergos an influence of the standard model interaction with the nuclear matter. The exact solutions for this equation and the electron energy spectrum in matter are obtained. This…
The present paper is the continuity of the previous papers "Non-linear field theory" I and II. Here on the basis of the electromagnetic representation of Dirac's electron theory we consider the geometrical distribution of the…
The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary transformation and shown to…
We suggest an alternative mathematical model for the electron in which the dynamical variables are a coframe (field of orthonormal bases) and a density. The electron mass and external electromagnetic field are incorporated into our model by…
Classical electromagnetism is linear. However, fields can polarize the vacuum Dirac sea, causing quantum nonlinear electromagnetic phenomena, e.g., scattering and splitting of photons, that occur only in very strong fields found in neutron…
We obtain novel nonlinear Schr\"{o}dinger-Pauli equations through a formal non-relativistic limit of appropriately constructed nonlinear Dirac equations. This procedure automatically provides a physical regularisation of potential…