A lattice Maxwell system is developed with gauge-symmetry, symplectic structure and discrete space-time symmetry. Noether's theorem for Lie group symmetries is generalized to discrete symmetries for the lattice Maxwell system. As a result, the lattice Maxwell system is shown to admit a discrete local energy-momentum conservation law corresponding to the discrete space-time symmetry. These conservative properties make the discrete system an effective algorithm for numerically solving the governing differential equations on continuous space-time. Moreover, the lattice model, respecting all conservation laws and geometric structures, is as good as and probably more preferable than the continuous Maxwell model. Under the simulation hypothesis by Bostrom and in consistent with the discussion on lattice QCD by Beane et al., the two interpretations of physics laws on space-time lattice could be essentially the same.
Since a classical charged point particle radiates energy and momentum it is argued that there must be a radiation reaction force. Here we present an action for the Maxwell-Lorentz without self interactions model, where each particle only responds to the fields of the other charged particles. The corresponding stress-energy tensor automatically conserves energy and momentum in Minkowski and other appropriate spacetimes.
This letter reports on a metriplectic formulation of collisional, nonlinear full-$f$ electromagnetic gyrokinetic theory compliant with energy conservation and monotonic entropy production. In an axisymmetric background magnetic field, the toroidal angular momentum is also conserved. Notably, a new collisional current, contributing to the gyrokinetic Maxwell-Ampère equation and the gyrokinetic charge conservation law, is discovered.
We construct an analytic solution to Maxwell's equations that violates global charge conservation, by building on the possibilities demonstrated in [Foundations of Physics 49, 330 (2019)]. The construction is valid for a spacetime containing a temporary singularity and a Maxwellian electrodynamics containing a proposed "topological" axion field. As such, it demonstrates that although "physics breaks down" at a singularity, the physical laws on the spacetime still impose constraints on what can happen. Further, the concepts of transformation optics can be applied to show that our specific mathe…
Though sufficient for local conservation of charge, we show that Maxwells displacement current is not necessary. An alternative to the Ampere Maxwell equation is exhibited and the alternative s electric and magnetic fields and scalar and vector potentials are expressed in terms of the charge and current densities. The alternative describes a theory in which action is instantaneous and so may provide a good approximation to Maxwells equations where and when the finite speed of light can be neglected. The result is reminiscent of the Darwin approximation which arose from the study classical char…
It is customary to assume that the law of conservation of the angular momentum is violated for an asymmetric energy-momentum tensors. This is the reason for criticizing the Minkowski tensor and other asymmetric energy-momentum tensors. In this paper, it is shown that the laws of conservation of energy and momentum following from an asymmetric tensor in the form of its total divergence are equivalent to the divergence of its symmetric part. It is shown that the total divergence of the antisymmetric part of the asymmetric tensor is identically zero. From this, it follows that for the asymmetric …
The Abraham--Minkowski controversy refers to a long-standing inability to adequately address certain issues involving the conservation of the momentum of an electromagnetic field in a linear dielectric medium. We apply the usual assumption of a material subsystem that couples to the electromagnetic subsystem such that the total energy and total momentum are conserved. We then construct the total energy--momentum tensor from the total energy density and the total momentum density. Applying conservation principles to the total energy--momentum tensor, we construct the tensor energy--momentum con…
The form of the energy-momentum tensor when a quasimonochromatic field propagates into and through an antireflection-coated, sourceless, transparent, continuous, linear magneto-dielectric medium, initially at rest in the local frame, remains controversial. The Minkowski energy-momentum tensor is the main component of the electromagnetic conservation law. It has been known for over a century that the electromagnetic conservation law is unsound as evidenced by alternative energy-momentum tensors that have been proposed to ameliorate known physical deficiencies (violation of conservation of angul…
We propose in this work the first symmetric hyperbolic system of conservation laws to describe viscoelastic flows of Maxwell fluids, i.e. fluidswith memory that are characterized by one relaxation-time parameter. Precisely, the system of quasilinear PDEs is detailed for the shallow-water regime, i.e. for hydrostatic incompressible 2D flows with free surface under gravity. It generalizes Saint-Venant system to viscoelastic flows of Maxwell fluids, and encompasses previous works with F. Bouchut. It also generalizes the (thin-layer) elastodynamics of hyperelastic materials to viscous fluids, and …
