Related papers: Comment on `Vector potential of the Coulomb gauge'
We show that the long-standing problem of gauge dependence of the effective potential arises due to the factorisation of the determinant of operators, which is invalid when we take the zeta-regularised trace of the operators. We show by…
Incremental models for magnetic vector hysteresis have been developed in previous works in accordance with basic principles of thermodynamics. In this paper, we present an equivalent representation of the associated hysteresis operator in…
The apparent nonlocality of the Coulomb gauge external field problem in electrodynamics is illustrated with an example in which nonlocality is especially striking. Explanation of this apparent nonlocal behaviour based on a purely local…
We study the abelian Higgs model out-of-equilibrium in two different approaches, a gauge invariant formulation, proposed by Boyanovsky et al. \cite{Boyanovsky:1996dc} and in the Coulomb gauge. We show that both approaches become equivalent…
We give a self contained presentation of the notion of variance of a vector field introduced by Jean Ecalle and Bruno Vallet in \cite{ev} following a previous work of Jean Ecalle and Dana Schlomiuk in \cite{es}. We give complete proofs and…
The Galilean gravitation derives from a scalar potential and a vector one. Poisson's equation to determine the scalar potential has no the expected Galilean covariance. Moreover, there are three missing equations to determine the potential…
Effective quantum field theoretical continuum models for graphene are investigated. The models include a complex scalar field and a vector gauge field. Different gauge theories are considered and their gap patterns for the scalar, vector,…
We present an alternative formulation of the magnetostatic boundary value problem which is useful for calculating the magnetic field around a magnetic material placed in the vicinity of steady currents. The formulation differs from the…
It is demonstrated how the right hand sides of the Lorentz Transformation equations may be written, in a Lorentz invariant manner, as 4--vector scalar products. The formalism is shown to provide a short derivation, in which the 4--vector…
The gravitational analog of the electromagnetic Poynting vector is constructed using the field equations of general relativity in the Hilbert gauge. It is found that when the gravitational Poynting vector is applied to the solution of the…
We calculate ab initio the gravitational potential energy per unit area for a gravitationally coupled multi-component galactic disk of stars and gas, which is given as the integration over vertical density distribution, vertical…
In this paper, we sketch and emphasize the automatic emergence of a quantum potential (QP) in general Hamilton-Jacobi equation via commuting relations, quantum canonical transformations and without the straight effect of wave function. The…
A procedure for solving the Maxwell equations in vacuum, under the additional requirement that both scalar invariants are equal to zero, is presented. Such a field is usually called a null electromagnetic field. Based on the complex Euler…
We present a computational methodology to directly calculate and visualize the directional components of the Coulomb, radiation, and total electromagnetic fields, as well as the scalar and vector potentials, generated by moving point…
We propose a reformulation of electrodynamics in terms of a {\it physical} vector potential entirely free of gauge ambiguities. Quantizing the theory leads to a propagator that is gauge invariant by construction in this reformulation, in…
The problem of a spinless particle subject to a general mixing of vector and scalar screened Coulomb potentials in a two-dimensional world is analyzed and its bounded solutions are found. Some unusual results, including the existence of a…
In the electromagnetic theory, the Hertz vector reduces the number of potentials in the free fields. The further advantage of this potential is that it is much easier to solve some radiation processes. It indicates that the related method…
A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and the…
In this work we revisit the process of constructing wave equations for the scalar and vector potentials of an electromagnetic field, and show that a wave equation with an arbitrary velocity (including a velocity higher than the velocity of…
It is shown that a Coulomb potential using a running coupling slightly modified from the perturbative form can produce an interquark potential that appears nearly linear over a large distance range. Recent high-statistics SU(2) lattice…