Related papers: Comments on "On vector potential of the Coulomb ga…
The notion that the electromagnetic field is quantised is usually inferred from observations such as the photoelectric effect and the black-body spectrum. However accounts of the quantisation of this field are usually mathematically…
The role of the measurement process in resolving the gauge ambiguity of the effective gravitational potential is reexamined. The motion of a classical point-like particle in the field of an arbitrary linear source, and in the field of…
We give a general expression for the static potential energy of the gravitational interaction of two massive particles, in terms of an invariant vacuum expectation value of the quantized gravitational field. This formula holds for…
The equation for the conic sections describing the possible orbits in a potential $V \sim r^{-1}$ is obtained by means of a vector constant of the motion differing from the traditional Laplace-Runge-Lenz vector.
In the self-sufficient potential formalism, treating all electromagnetic phenomena as natural or forced oscillations of some distributed electromagnetic oscillating system (Minkowski space-time), the electromagnetic potential must be…
The vector potential for the Ohmic heating coil system of a tokamak is obtained in semi-analytical form. Comparison is made to the potential of a simple, finite solenoid. In the quasi-static limit, the time rate of change of the potential…
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…
Equilibria of polygonal linkage with respect to Coulomb potential of point charges placed at the vertices of linkage are considered. It is proved that any convex configuration of a quadrilateral linkage is the point of global minimum of…
We analyze the conclusions of the influence of a Coulomb-type potential on the Klein-Gordon oscillator. We show that the truncation method proposed by the authors do not yield all the eigenvalues of the radial equation but just one of them…
The expression for the electromagnetic field of a charge moving along an arbitrary trajectory is obtained in a direct, elegant, and Lorentz invariant manner without resorting to more complicated procedures such as differentiation of the…
The property of isotonicity of a continuous convex function defined on the entire space or only on the positive cone is characterized via subdifferentials. Numerous examples illustrating the obtained results are included.
Using a gauge covariant operator technique we deduce the path integral for a charged particle in a stationary magnetic field, verifying the "midpoint rule" for the discrete form of the interaction term with the vector potential.
We discuss the Kirchhoff gauge in classical electrodynamics. In this gauge the scalar potential satisfies an elliptical equation and the vector potential satisfies a wave equation with a nonlocal source. We find the solutions of both…
The length gauge uses a scalar potential to describe a laser field, thus treating it as a longitudinal field rather than as a transverse field. This distinction is revealed in the fact that the Maxwell equations that relate to the length…
Results obtained for the antisymmetric gauge A=[Hy,-Hx]/2 by Brown and Zak are compared with those based on pure group-theoretical considerations and corresponding to the Landau gauge A=[0,Hx]. Imposing the periodic boundary conditions one…
The authors claim to have found a "proper", "gauge-invariant" definition of a charged-particle's momentum in gauge theory, which is more "superior" than the textbook version. I show that their result arises from a misunderstanding of gauge…
A survey of the stability of matter problem is given, starting with the stability of the hydrogen atom. The stablity of bulk matter with Coulomb potentials, with or without relativistic mechanics, and with or without magnetic fields is…
In this paper our aim is to present some monotonicity and convexity properties for the one dimensional regularization of the Coulomb potential, which has applications in the study of atoms in magnetic fields and which is in fact a…
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The…
A generalized translational invariant noncommutative field theory is analyzed in detail, and a complete description of translational invariant noncommutative structures is worked out. The relevant gauge theory is described, and the planar…