Related papers: Covariant conservation laws, local invariance and …
We investigate the question of how the knowledge of sufficiently many local conservation laws for a model can be utilized to solve the model. We show that for models where the conservation laws can be written in one-sided forms, like…
Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and…
For k-symplectic Hamiltonian field theories, we study infinitesimal transformations generated by certain kinds of vector fields which are not Noether symmetries, but which allow us to obtain conservation laws by means of a suitable…
Conservation laws in ideal gas dynamics and magnetohydrodynamics (MHD) associated with fluid relabelling symmetries are derived using Noether's first and second theorems. Lie dragged invariants are discussed in terms of the MHD Casimirs. A…
Though a global Chern-Simons (2k-1)-form is not gauge invariant, this form seen as a Lagrangian of higher-dimensional gauge theory leads to the conservation law of a modified Noether current.
A construction of conservation laws and conserved quantities for perturbations in arbitrary metric theories of gravity is developed. In an arbitrary field theory, with the use of incorporating an auxiliary metric into the initial Lagrangian…
The conservation laws of nonrelativistic and relativistic systems are reviewed and some simple illustrations are provided for the restrictive nature of the relativistic conservation law involving the center of energy compared to the…
Using a manifestly invariant Lagrangian density based on Clebsch fields and suitable for geophysical fluid dynamics, the conservation of mass, entropy, momentum and energy, and the associated symmetries are investigated. In contrast, it is…
The study of problems of the calculus of variations with compositions is a quite recent subject with origin in dynamical systems governed by chaotic maps. Available results are reduced to a generalized Euler-Lagrange equation that contains…
A variational principle for Lagrangian densities containing derivatives of real order is formulated and the invariance of this principle is studied in two characteristic cases. Necessary and sufficient conditions for an infinitesimal…
Quasi-Noether differential systems are more general than variational systems and are quite common in mathematical physics. They include practically all differential systems of interest, at least those that have conservation laws. In this…
This paper establishes a second vanishing theorem for formal local cohomology modules over Noetherian local rings. We introduce the \textit{formal dimension} invariant and characterize the vanishing of higher formal local cohomology in…
In this paper, the local inertial coordinate system is calculated through coordinate transformations from laboratory coordinate system. We derived the same free falling equations as those in General Relativity. However, the definitions of…
A simple theorem is proved: When a gauge-invariant local field theory is written in terms of matter fields alone, a composite gauge boson or bosons must be formed dynamically. The theorem results from the fact that the Noether current…
English version of abstract: The dynamic optimization problems treated by the calculus of variations are usually solved with the help of the 2nd order Euler-Lagrange differential equations. These equations are, generally speaking,…
This article uses Cartan-K\"ahler theory to construct local conservation laws from covariantly closed vector valued differential forms, objects that can be given, for example, by harmonic maps between two Riemannian manifolds. We apply the…
It is shown that the zilch conservation law arises as the Noether current corresponding to a variational symmetry of a duality-symmetric Maxwell Lagrangian. The action of the corresponding symmetry generator on the duality-symmetric…
We review the formulation of a Lorentz-covariant bispinorial wave function and wave equation for a single photon on a flat background. We show the existence of a 10-dimensional set of conservation laws for this equation, and prove that 8 of…
Based on the principle of relativity, we find that the sufficient and necessary condition for the general covariance of a field theory actually requires more than the invariance of its local Langrangian density. If the spacetime is not a…
A class of generalized Galileon cosmological models, which can be described by a point-like Lagrangian, is considered in order to utilize Noether's Theorem to determine conservation laws for the field equations. In the…