相关论文: Weber-like interactions and energy conservation

Conservation laws are formulated for systems of differential equations by using symmetries and adjoint symmetries, and an application to systems of evolution equations is made, together with illustrative examples. The formulation does not…

In this paper, we are concerned with the minimal regularity of weak solutions implying the law of balance for both energy and helicity in the incompressible Euler equations. In the spirit of recent works due to Berselli [5] and…

Maxwell's macroscopic equations combined with a generalized form of the Lorentz law of force are a complete and consistent set of equations. Not only are these five equations fully compatible with special relativity, they also conform with…

We offer a concise and direct way to derive the bending angle of light (i.e. as generally called, gravitational lensing), while light grazes a star, through the approach suggested earlier by the first author, which is fundamentally based on…

We apply the principle of energy conservation to the motion of the test particle in gravitational field by requiring that its energy, gained by gravitation, has to be balanced by decrease of its rest mass. Due to the change of mass in…

This paper presents an overview of the derivation and significance of recently derived conservation laws for the matrix moments of Hermitean random matrices with dominant exponential weights that may be either even or odd. This is based on…

In a previous paper, the authors with Ann Nelson proposed that the UV and IR applicability of effective quantum field theories should be constrained by requiring that strong gravitational effects are nowhere encountered in a theory's domain…

Many-body quantum-mechanical stationary states that have real valued wavefunctions are shown to satisfy a classical conservation of energy equation with a kinetic energy function. The terms in the equation depend on the probability…

We conjecture that the modified commutation relations suggested in the context of quantum gravity (QG) persist also in the classical limit, if the momentum of the classical object is not too large, and calculate the corresponding perihelion…

The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding…

We consider modified theories of gravity with a direct coupling between matter and geometry, denoted by an arbitrary function in terms of the Ricci scalar. Due to such a coupling, the matter stress tensor is no longer conserved and there is…

We consider the motion of a point particle in a stationary spacetime under the influence of a scalar, electromagnetic or gravitational self-force. We show that the conservative piece of the first-order self-force gives rise to Hamiltonian…

The interactions of gravitational waves with interstellar matter, dealing with resonant wave-particle and wave-wave interactions, are considered on the basis of magnetic-type Maxwell-Vlasov equations. It is found that the behavior of the…

In this article we focus our attention on the principle of energy conservation within the context of systems of fluid dynamics. We give an overview of results concerning the resolution of the famous Onsager conjecture - which states…

We show for a variety of classes of conservative PDEs that discrete gradient methods designed to have a conserved quantity (here called energy) also have a time-discrete conservation law. The discrete conservation law has the same conserved…

Even though the energy carried by a gravitational wave is not itself gauge invariant, the interaction with a gravitational antenna of the gravitational wave which carries that energy is. It therefore has to be possible to make some…

The cosmological backreaction from perturbations is clearly gauge-dependent, and obviously depends on the choice of averaged Hubble rate. We consider two common choices of Hubble rate and advocate the use of comoving volume-preserving…

We revisit the Scalar Weak Gravity Conjecture and investigate the possibility to impose that scalar interactions dominate over gravitational ones. More precisely, we look for consequences of assuming that, for leading scalar interactions,…

In this paper, we prove the energy conservation for the weak solutions to the three-dimensional equations of compressible magnetohydrodynamic flows (MHD) under certain conditions only about density and velocity. This work is inspired by the…

We argue that conservation laws based on the local matter-only stress-energy-momentum tensor (characterized by energy and momentum per unit volume) cannot adequately explain a wide variety of even very simple physical phenomena because they…