相关论文: The Kirchhoff gauge

A class of gauges for the Einstein vacuum equations is introduced, along with three symmetric hyperbolic systems. The first implies the local realizability of the gauge. The second is the dynamical subset of the field equations. The third…

We investigate the coupling of the electromagnetic sources (charge and current densities) to the scalar and vector potentials in classical electrodynamics, using Green function techniques. As is well known, the scalar potential shows an…

The problem of defining a gauge invariant effective potential with a strict energetic interpretation is examined in the context of spontaneously broken gauge theories. It is shown that such a potential can be defined in terms of a composite…

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…

Wave/Schr\"{o}dinger equations with potentials naturally originates from both the quantum physics and the study of nonlinear equations. The distractive Coulomb potential is a quantum mechanical description of distractive Coulomb force…

A specific choice of gauge is shown to imply a decoupling between the tensor and scalar components of Gravitational Radiation in the context of Brans-Dicke type theories of gravitation. The comparison of the predictions of these theories…

Scalar Quantum Electrodynamics is investigated in the Heisenberg picture via the Duffin-Kemmer-Petiau gauge theory. On this framework, a perturbative method is used to compute the vacuum polarization tensor and its corresponding induced…

In this work we deal with elliptic equations driven by the variable exponent double phase operator with a Kirchhoff term and a right-hand side that is just locally defined in terms of very mild assumptions. Based on an abstract critical…

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…

We show that the gauge hierarchy problem can be solved in the framework of scalar-tensor theories of gravity very much in the same way as it is solved in the Randall-Sundrum scenario. Our solution involves a fine-tuning of the gravitational…

The Cauchy problem for the scalar wave equation in the Kerr geometry is considered, with initial data which is smooth and compactly supported outside the event horizon. A time-independent energy estimate for the outgoing wave is obtained.…

We show that the incompressible Euler equations in three spatial dimensions can be expressed in terms of an abelian gauge theory with a topological BF term. A crucial part of the theory is a 3-form field strength, which is dual to a…

We study a superlinear and subcritical Kirchhoff type equation which is variational and depends upon a real parameter $\lambda$. The nonlocal term forces some of the fiber maps associated with the energy functional to have two critical…

A unified formulation of rigid body dynamics based on Gauss principle is proposed. The Lagrange, Kirchhoff and Newton-Euler equations are seen to arise from different choices of the quasicoordinates in the velocity space. The…

The Coulomb-gauge vector potential of a uniformly moving point charge is obtained by calculating the gauge function for the transformation between the Lorenz and Coulomb gauges. The expression obtained for the difference between the vector…

There is undetermined potential function $V(\phi)$ in the action of mimetic gravity which should be resolved through physical means. In general relativity(GR), the static spherically symmetric(SSS) solution to the Einstein equation is a…

Clebsch potential gauge field theory for magnetohydrodynamics is developed based in part on the theory of Calkin (1963). It is shown how the polarization vector ${\bf P}$ in Calkin's approach, naturally arises from the Lagrange multiplier…

We extend previous work [arXiv:1908.09095] to the case of Maxwell's equations with a source. Our work shows how to construct a retarded vector potential for the Maxwell field on the Kerr-Newman background in a radiation gauge. As in our…

Three-dimensional scalar electrodynamics, with a local U(1) gauge symmetry, is believed to be dual to a scalar theory with a global U(1) symmetry, near the phase transition point. The conjectured duality leads to definite predictions for…

This is the second and last paper of a series aimed at solving the local Cauchy problem for polarized $\mathbb U(1)$ symmetric solutions to the Einstein vacuum equations featuring the nonlinear interaction of three small amplitude impulsive…