Related papers: A Non-Newtonian Noether's Symmetry Theorem

We disscuss some geometric aspects of the concept of non-Noether symmetry. It is shown that in regular Hamiltonian systems such a symmetry canonically leads to a Lax pair on the algebra of linear operators on cotangent bundle over the phase…

We show that all Lie point symmetries of various classes of nonlinear differential equations involving critical nonlinearities are variational/divergence symmetries.

Given a quantum system consisting of many parts, we show that symmetry of the system's state, i.e., invariance under swappings of the subsystems, implies that almost all of its parts are virtually identical and independent of each other.…

This paper expounds the modern theory of symplectic reduction in finite-dimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved quantities, i.e. Noether's theorem. It…

We argue that the variational calculus leading to Euler's equations and Noether's theorem can be replaced by equivariance and invariance conditions avoiding the action integral. We also speculate about the origin of Lagrangian theories in…

On the basis of gauge principle in the field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized…

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…

We explicitly derive, following a Noether-like approach, the criteria for preserving Poincare invariance in noncommutative gauge theories. Using these criteria we discuss the various spacetime symmetries in such theories. It is shown that,…

Noether's Theorem is familiar to most physicists due its fundamental role in linking the existence of conservation laws to the underlying symmetries of a physical system. Typically the systems are described in the particle-based context of…

A class of autonomous, even-order ordinary differential equations is discussed from the point of view of Lie symmetries. It is shown that for a certain power nonlinearity, the Noether symmetry group coincides with the Lie point symmetry…

Noether symmetry for higher order gravity theory has been explored, with the introduction of an auxiliary variable which gives the only correct quantum desccription of the theory, as shown in a series of earlier papers. The application of…

In this paper, within the framework of the consistent approach recently introduced for approximate Lie symmetries of differential equations, we consider approximate Noether symmetries of variational problems involving small terms. Then, we…

It is shown that using Noether's Theorem explicitly employing gauge invariance for variations of the electromagnetic four-potential $A^\mu$ straightforwardly ensures that the resulting electromagnetic energy-momentum tensor is symmetric.…

Famously, Klein and Einstein were embroiled in an epistolary dispute over whether General Relativity has any physically meaningful conserved quantities. In this paper, we explore the consequences of Noether's second theorem for this debate,…

Noether's theorem provides a powerful link between continuous symmetries and conserved quantities for systems governed by some variational principle. Perhaps unfortunately, most dynamical systems of interest in neuroscience and artificial…

Using the commutativity of a general variation with the time differentiation we discuss both global and local (gauge) symmetries of a lagrangian from a unified point of view. The Noether considerations are thereby applicable for both cases.…

Based on a general variational principle, Noether's theorem is revisited. It is shown that the so called pseudotensor problem of the gravitational energy-momentum is a result of mis-reading Noether's theorem, and in fact, all the Noether's…

All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted…

Noether theorem establishes an interesting connection between symmetries of the action integral and conservation laws of a dynamical system. The aim of the present work is to classify the damped harmonic oscillator problem with respect to…

Any symmetry reduces a second-order differential equation to a first-order equation: variational symmetries of the action (exemplified by central field dynamics) lead to conservation laws, but symmetries of only the equations of motion…