Related papers: A Direct Method for Obtaining the Differential Con…
It is prove, that the gravity field energy formulas obtained for static systems on the ground of local energy conservation law by test-particles fall, is suitable for stationary systems.
We prove that under certain assumptions a partial differential equation can be derived from a variational principle. It is well-known from Noether's theorem that symmetries of a variational functional lead to conservation laws of the…
We describe a new method which allows us to obtain a result of exact controllability to trajectories of multidimensional conservation laws in the context of entropy solutions and under a mere non-degeneracy assumption on the flux and a…
In this paper, we review two related aspects of field theory: the modeling of the fields by means of exterior algebra and calculus, and the derivation of the field dynamics, i.e., the Euler-Lagrange equations, by means of the stationary…
We develope a difference calculus analogous to the differential geometry by translating the forms and exterior derivatives to similar expressions with difference operators, and apply the results to fields theory on the lattice [Ref. 1]. Our…
We derive conservation laws for energy-momentum (canonical and dynamical) and angular momentum for a general Lorentz connection.
We provide an informal overview on the theory of transport equations with non smooth velocity fields, and on some applications of this theory to the well-posedness of hyperbolic systems of conservation laws.
Reciprocal transformations associated with admitted conservation laws were originally used to derive invariance properties in non-relativistic gasdynamics and applied to obtain reduction to tractable canonical forms. They have subsequently…
Electromagnetic fields of an accelerated charge are derived from the first principles using Coulomb's law and the relativistic transformations. The electric and magnetic fields are derived first for an instantaneous rest frame of the…
Some problems on variations are raised for classical discrete mechanics and field theory and the difference variational approach with variable step-length is proposed motivated by Lee's approach to discrete mechanics and the difference…
We introduce a method to construct conservation laws for a large class of linear partial differential equations. In contrast to the classical result of Noether, the conserved currents are generated by any symmetry of the operator, including…
In this short review we present a self-contained exposition of the effective field theory method approach to model the dynamics of gravitationally bound compact binary systems within the post-Newtonian approximation to General Relativity.…
Starting from the most general formulation of stochastic thermodynamics---i.e. a thermodynamically consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs---, we define a procedure to identify the…
For a system of partial differential equations that has an extended Kovalevskaya form, a reduction procedure is presented that allows one to use a local (point, contact, or higher) symmetry of a system and a symmetry-invariant conservation…
We derive the Lorentz self force for an arbitrarily moving charged particle via averaging the retarded fields. The derivation is simple and at the same time pedagogically accessible. We obtain the radiation reaction for a charged particle…
The concept of photon is not necessary only applied to the relativistic Doppler theory. It may also work well for classical theory. As conservation of momentum and energy are physical laws, if applying these laws gives the exact…
As is well known, in order for the Einstein--Hilbert action to have a well defined variation, and therefore to be used for deriving field equation through the stationary action principle, it has to be amended by the addition of a suitable…
The general, linear equations with constant coefficients on quantum Minkowski spaces are considered and the explicit formulae for their conserved currents are given. The proposed procedure can be simplified for *-invariant equations. The…
The purpose of this paper is to present a Lagrangian from which we can derive the quantionic field equation written in the Dirac gauge using the principle of stationary action.
Scalar-tensor theories have drawn the attention of cosmologist for the past few years because they can provide mechanism to explain the observable phenomena. Moreover, the results of scalar-tensor theories can be applied in higher-order…