Related papers: Noether Theorems and Reality of Motion
An important methodological problem of theoretical mechanics related to inertia is discussed. Analysis Inertia is performed in four-dimensional Minkowski space-time based on the law of conservation of energy-momentum. This approach allows…
Motivated by various theoretical arguments that the Planck energy (Ep - 10^19 GeV) - should herald departures from Lorentz invariance, and the possibility of testing these expectations in the not too distant future, two so-called "Doubly…
This paper explores exact cosmological solutions of anisotropic universe model through Noether symmetry technique in energy-momentum squared gravity. This theory resolves the primordial singularity and provides viable cosmological…
Noether's celebrated theorem associating symmetry and conservation laws in classical field theory is adapted to allow for broken symmetry in geometric mechanics and is shown to play a central role in deriving and understanding the…
For a field theory that is invariant under diffeomorphisms there is a subtle interplay between symmetries, conservation laws and the phase space of the theory. The natural language for describing these ideas is that of differential forms…
In this work we revisit the study of the gravitational interaction in the context of the Special Theory of Relativity. It is found that, as long as the equivalence principle is respected, a relativistic non-linear energy conservation…
In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable (vector) density is known to generate the so--called {\em conserved Noether currents}. It turns out that along any section of the relevant…
The main objective of this article is to examine some physically viable solutions through the Noether symmetry technique in $f(R, T^{2})$ theory. For this purpose, we assume a generalized anisotropic and homogenous spacetime that yields…
The universal principle obtained by Emmy Noether in 1918, asserts that the invariance of a variational problem with respect to a one-parameter family of symmetry transformations implies the existence of a conserved quantity along the…
Conservation laws related to the gauge invariance of Lagrangians and Euler-Lagrange operators in finite and infinite order Lagrangian formalisms are analyzed.
The principle of energy conservation is widely taken to be a serious difficulty for interactionist dualism (whether property or substance). Interactionists often have therefore tried to make it satisfy energy conservation. This paper…
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 analyze a category of problems that is of interest in many physical situations, including those encountered in introductory physics classes: systems with two well-delineated parts that exchange energy, eventually reaching a shared…
We briefly recall the problem of defining conserved quantities such as energy in general relativity, and the solution by introducing a symmetric background. We apply the general formalism to perturbed Robertson-Walker spacetimes with de…
We revisit the old problem of the energy-momentum tensor in general relativistic field theories. On the basis of the general covariance we derive a simple equation for the Hilbert and Noether energy-momentum tensors for the scalar and…
We first see that the inertia of Newtonian mechanics is absolute and troublesome. General relativity can be viewed as Einstein's attempt to remedy, by making inertia relative, to matter---perhaps imperfectly though, as at least a couple of…
A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational…
In this paper using a Clifford bundle formalism we examine (a): the strong conditions for existence of conservation laws involving only the energy-momentum and angular momentum of the matter fields on a general Riemann-Cartan spacetime and…
We begin by presenting the classical deterministic problems of the calculus of variations, with emphasis on the necessary optimality conditions of Euler-Lagrange and the Noether theorem. As examples of application, we obtain the…
In Newtonian gravity it is a moot question whether energy should be localized in the field or inside matter. An argument from relativity suggests a compromise in which the contribution from the field in vacuum is positive definite. We show…