Related papers: Comments on "On vector potential of the Coulomb ga…
This is an introduction to a provisional mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ supersymmetric gauge theories, studied in arXiv:1503.03676, arXiv:1601.03586
We discuss the semi-classical gravitational wave corrections to Gauss's law, and obtain an explicit solution for the electromagnetic potential. The Gravitational Wave perturbs the Coulomb potential with a function which propagates to the…
The Coulomb energy of a charge that is uniformly distributed on some set is maximized (among sets of given volume) by balls. It is shown here that near-maximizers are close to balls.
Gauge transformation leaves the electric and the magnetic fields unchanged as long as the gauge function is treated classically. In this paper we consider the gauge transformation commonly used to obtain the electric dipole interaction…
The vector nature of magnetic fields and the geometrical interpretation of gravity introduced by general relativity, guarantee a special coupling between magnetism and spacetime curvature. This magneto-geometrical interaction effectively…
The Lorentz force can be obtained from Maxwell's equations in the Coulomb gauge provided that we assume that the electric portion of the force acted on a charge is known, and the magnetic component is perpendicular to the velocity of motion…
Maxwell-Lorenz theory describes only vortex electromagnetic processes. Potential component of the magnetic field is usually excluded by the introduction of mathematical terms: Coulomb and Lorenz gauges. Proposed approach to the construction…
We numerically calculate the energy and momentum transfer rates due to Coulomb scattering between two fluids moving with a relative velocity. The results are fitted by simple functions. The fitting formulae are useful to simulate outflows…
The original ideas about noncommuting coordinates are recalled. The connection between U(1) gauge fields defined on noncommuting coordinates and fluid mechanics is explained.
In this expository review we discuss various aspects of gauge theory. While the focus is on mathematics, wherever possible we make contact with theoretical high energy physics. Particular emphasis is placed on instantons and monopoles,…
We have analyzed Coulomb drag between currents of interacting electrons in two parallel one-dimensional conductors of finite length $L$ attached to external reservoirs. For strong coupling, the relative fluctuations of electron density in…
How quantum tunneling will behave when the singularity is preserved as much as possible is the main question of this paper. We get that the Coulomb sibgularity is reflected as infinitly accelerated oscillations in the transmission…
This is an introduction to a provisional mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ supersymmetric gauge theories, studied in arXiv:1503.03676, arXiv:1601.03586. This is an expanded version of an article…
We perform $SU(2)$ Yang-Mills lattice simulation of the electric field distribution in the Coulomb gauge for different values of $\beta$ to further investigate the nature of the Coulomb flux tube.
It is shown that relative coordinate and momentum of coherent electron pair have the meaning of observables with the help of quadrupole and magnetic moments. Distributions of quadrupole terms of scalar potential are shown. These…
In seeking a minimal variational formulation of Maxwell's equations, one is led naturally to the scalar and vector potentials as "adjoint" functions in a well-defined sense and to the crucial minus sign that defines the Lagrangian.
It is discussed the singular string associated to the gauge field of monopoles must be a physical observable if the monopole charge is different from zero. It is naturally found that if the gauge is to be an observable, it is possibly…
At 2-loop order in the Coulomb gauge, individual Feynman graphs contributing to the effective action have energy divergences. It is proved that these cancel in suitable combinations of graphs. This has previously been shown only for…
These are (somewhat informal) lectures notes for the CIME summer school "Geometric Representation Theory and Gauge Theory" in June 2018. In these notes we review the results and constructions of a series of our joint papers with H.Nakajima…
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…