Related papers: New solutions to an old equation
Just after the Dirac equation was established, a number of physicists tried to comment on and solve the spectral problem for the Dirac Hamiltonian with the Coulomb field of arbitrarily large charge $Z$, especially with $Z$ that is more than…
Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…
Two different algebras are applied to the system of charges. Such generalizations of classical theory eliminate infinite seif-energy of electrons. Paradoxical radiative self-acceleration of an electron is also eliminated in this way. One of…
We solve the Dirac equation in one space dimension for the case of a linear, Lorentz-scalar potential. This extends earlier work of Bhalerao and Ram [Am. J. Phys. 69 (7), 817-818 (2001)] by eliminating unnecessary constraints. The spectrum…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
A detailed study is made of the space-time transformation properties of intercharge forces and the associated electric and magnetic force fields, both in classical electrodynamics and in a recently developed relativistic classical…
The solutions of the classical equations of motion on a periodic lattice are found which correspond to abelian single and double Dirac sheets. These solutions exist also in non--abelian theories. Possible applications of these solutions to…
In the classical vacuum Maxwell-Lorentz theory the self-force of a charged point particle is infinite. This makes classical mass renormalization necessary and, in the special relativistic domain, leads to the Abraham-Lorentz-Dirac equation…
This paper continues the author's work \cite{PartI}, where a new framework of the matter-induced physical geometry was built and an intrinsic nonlinearity of the Dirac equation discovered. Here, the nonlinear Dirac equation is solved and…
We investigate the solutions to the Lorentz-Dirac equation and show that its solution flow has a structure identical to the one of renormalization group flows in critical phenomena. The physical solutions of the Lorentz-Dirac equation lie…
We investigate the classical ground state of a large number of charges confined inside a disk and interacting via the Coulomb potential. By realizing the important role that the peripheral charges play in determining the lowest energy…
The classical Avez-Seifert theorem is generalized to the case of the Lorentz force equation for charged test particles with fixed charge-to-mass ratio. Given two events x_{0} and x_{1}, with x_{1} in the chronological future of x_{0}, and a…
It is shown, by a semi-classical argument, that the Dirac charge quantization is still valid in the (classical) Born-Infeld electromagnetic theory. Then it is possible to calculate Dirac's monopole mass in the framework of this theory,…
The stopping power and energy loss rate of charged particles traversing a two-dimensional Dirac plasma is investigated. The Dirac plasma considered here models a solid state system, recently realized graphene monolayer, where the conduction…
A formulation of classical electrodynamics on an energy-momentum background of constant, non-zero curvature is given. The procedure consists of taking the formulation of standard electrodynamics in the energy-momentum representation, and…
The power radiated by a moving charge is given by Larmor's formula which can be derived by integrating the Li\'enard-Wiechert potential over the whole past history of the charge. However, extracting the same result from the…
The physicists of the early 20th century were unaware of two ideas which are vital to understanding some aspects of modern physics within classical theory. The two ideas are: 1) the presence of classical electromagnetic zero-point…
It is shown that the calculation of Dirac operator for the spherical coordinate system with spherical Dirac matrices and using the spin connection formalism is in the contradiction with the definition of standard Dirac operator in the…
The classic image problem in electromagnetism involves a grounded infinite conducting plane and a point charge. The force of attraction between the point charge and the plane is identified using an equivalent-field picture of an image…
We review the formulation of the problem of the electromagnetic self-interaction of a relativistic charged particle in the framework of the manifestly covariant classical mechanics of Stueckelberg, Horwitz and Piron. The gauge fields of…