相关论文: Lorenz or Coulomb in Galilean Electromagnetism ?

There is a simple formula for the gauge function of the transformation from the Lorenz gauge to the Coulomb gauge, valid under a condition that is satisfied by some charge densities employed in the literature. An equation for the gauge…

This article is dedicated to Elliott Lieb in celebration of his 90th birthday. I recount briefly some history of our joint work on the existence of the thermodynamic limit for Coulomb systems and discuss, even more briefly, two open…

The Liouville equation with non-constant magnetic field is obtained as a limit in the Planck constant \hbar of the Heisenberg equation with the same magnetic field. The convergence is with respect to an appropriate semi-classical pseudo…

The Bohr-van Leeuwen theorem is often summarized as saying that there is no classical magnetic susceptibility, in particular no diamagnetism. This is seriously misleading. The theorem assumes position dependent interactions but this is not…

We show that if Maxwell's equations are expressed in a form independent of specific units, at least three Galilean limits can be extracted. The electric and magnetic limits can be regarded as nonrelativistic limits because they are obtained…

We consider the contribution of electron-electron interactions to the orbital magnetization of a two-dimensional electron gas, focusing on the ballistic limit in the regime of negligible Landau-level spacing. This regime can be described by…

In an earlier paper we provided an alternative to the standard gauge concept for deriving the classical electromagnetic wave equations. This alternative involves recognition of two previously overlooked basic equations and represents a…

We consider the non-linear classical field theory which results from adding to the Maxwell's Lagrangian the contributions from the weak-field Euler-Heisenberg Lagrangian and a non-uniform part which involves derivatives of the electric and…

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…

The classical theory of electromagnetism has been revisited and the possibility of longitudinal photon wave is explored. It is shown that the emergence of longitudinal wave is a consequence of Lorenz gauge (condition) violation. Proca,…

A theory of electromagnetism is proposed that is based on the Fermi Lagrangian, which is symmetric under electromagnetic spin rotation. Its features are: - the four-potential is unambiguously determined by the inhomogeneous wave equation…

It is shown that a nonrelativistic mechanical system involving a general nonrelativistic potential V(|r1-r2|) between point particles at positions r1 and r2 can be extended to a Lagrangian system which is invariant under Lorentz…

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…

Following a recent method introduced by C. Hainzl, J.P. Solovej and the second author of this article, we prove the existence of the thermodynamic limit for a system made of quantum electrons, and classical nuclei whose positions and…

The concept of gauge invariance in classical electrodynamics assumes tacitly that Maxwell's equations have unique solutions. By calculating the electromagnetic field of a moving particle both in Lorenz and in Coulomb gauge and directly from…

The four (electro-magnetic, weak, strong and gravitational) interactions are described by singular Lagrangians and by Dirac-Bergmann theory of Hamiltonian constraints. As a consequence a subset of the original configuration variables are…

The Lorentz law of force is the fifth pillar of classical electrodynamics, the other four being Maxwell's macroscopic equations. The Lorentz law is the universal expression of the force exerted by electromagnetic fields on a volume…

The expression for the Coulomb-gauge vector potential in terms of the `instantaneous' magnetic field derived by Stewart [2003 Eur. J. Phys. 24, 519] by employing Jefimenko's equation for the magnetic field and Jackson's formula for the…

The relativistic bound-state energy spectrum and the wavefunctions for the Coulomb potential are studied for de Sitter and anti-de Sitter spaces in the context of the extended uncertainty principle. Klein-Gordon and Dirac equations are…

If potential energy is the timelike component of a four-vector, then there must be a corresponding spacelike part which would logically be called the potential momentum. The potential four-momentum consisting of the potential momentum and…