Related papers: Note on the Dirac Field in Real Domain
We demonstrate that neutral Dirac particles in external electric fields, which are equivalent to generalized Dirac oscillators, are physical examples of quasi-exactly solvable systems. Electric field configurations permitting quasi-exact…
The article provides proofs for the regularity of Dirac eigenfunctions, subject to MIT boundary conditions employed on various types of open sets ranging from smooth ones to convex polygons in two dimensions, as well as on half-space and…
An accelerating electric charge coupled to its own electromagnetic (EM) field both emits radiation and experiences the radiation's reaction as a (self-)force. Considering the system from an Effective Field Theory perspective, and using the…
We propose a simple relativistic derivation of the electric and the magnetic fields generated by an electric point charge moving with constant velocity. Our approach is based on the radar detection of the point space coordinates where the…
We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…
A simple translation between a standard representation of $\mathfrak{sl}_2\mathbb{C}$ and the complex-quaternions ($\mathbb{H}\otimes_\mathbb{R}\mathbb{C}$) is established and exploited to construct a novel hyper-complex description of the…
We consider the magnetic Dirac operator on a curved strip whose boundary carries the infinite mass boundary condition. When the magnetic field is large, we provide the reader with accurate estimates of the essential and discrete spectra. In…
We construct Dirac-like equation for describing two-level atom interacting with resonant laser field.
Previously (A. Akhmeteli, J. Math. Phys., v. 52, p. 082303 (2011)), the Dirac equation in an arbitrary electromagnetic field was shown to be generally equivalent to a fourth-order equation for just one component of the four-component Dirac…
The expression for the intensity of the electromagnetic field radiation is derived in the approximation next to the dipole one. The presented approach is based on fundamental equations from the introductory course on classical…
We provide some new necessary and sufficient conditions which guarantee arbitrary pole placement of a particular linear system over the complex numbers. We exhibit a non-trivial real linear system which is not controllable by real static…
Effects of the quadratic interaction term in the real Dirac field theory are considered.
By requiring the linear differential operator in Newton's law of motion to be self adjoint, we obtain the field equation for the linear theory, which is the classical electrodynamics. In the process, we are also led to a fundamental…
We formulate explicitly the necessary and sufficient conditions for the local invertibility of a field transformation involving derivative terms. Our approach is to apply the method of characteristics of differential equations, by treating…
The Born-Infeld form of the hydrogen atom has a spectrum that can be used to determine the physical viability of the theory, and place an experimentally relevant bound on the single parameter found in it. We compute this spectrum using the…
We present a variational formulation of electrodynamics using de Rham even and odd differential forms. Our formulation relies on a variational principle more complete than the Hamilton principle and thus leads to field equations with…
We derive a modified non-perturbative Lorentz-Abraham-Dirac equation. It satisfies the proper conservation laws, particularly, it conserves the generalized momentum, the latter property eliminates the symmetry-breaking runaway solution. The…
We develop a quaternionic electrodynamics and show that it naturally supports the existence of magnetic monopoles. We obtained the field equations, the continuity equation, the electrodynamic force law, the Poynting vector, the energy…
We show that the energy spectrum of the one-dimensional Dirac equation in the presence of a spatial confining point interaction exhibits a resonant behavior when one includes a weak electric field. After solving the Dirac equation in terms…
We extend the biquaternionic Dirac equation to include interactions with a background bosonic field. The obtained biquaternionic Dirac equation yields Maxwell-like equations that hold for both a matter field and an electromagnetic field.…