Related papers: Noether's Theorem for a Fixed Region
The relationship between symmetry fields and first integrals of divergence-free vector fields is explored in three dimensions in light of its relevance to plasma physics and magnetic confinement fusion. A Noether-type Theorem is known: for…
The first part of this paper develops a geometric setting for differential-difference equations that resolves an open question about the extent to which continuous symmetries can depend on discrete independent variables. For general…
Noether's theorem is a fundamental result in physics stating that every symmetry of the dynamics implies a conservation law. It is, however, deficient in several respects: (i) it is not applicable to dynamics wherein the system interacts…
We prove a theorem concerning the Noether symmetries for the area minimizing Lagrangian under the constraint of a constant volume in an n-dimensional Riemannian space. We illustrate the application of the theorem by a number of examples.
Noether's theorem is reviewed with a particular focus on an intermediate step between global and local gauge and coordinate transformations, namely linear transformations. We rederive the well known result that global symmetry leads to…
We provide a geometric extension of the generalized Noether theorem for scaling symmetries recently presented in \cite{zhang2020generalized}. Our version of the generalized Noether theorem has several positive features: it is constructed in…
When discussing consequences of symmetries of dynamical systems based on Noether's first theorem, most standard textbooks on classical or quantum mechanics present a conclusion stating that a global continuous Lie symmetry implies the…
We prove a fractional Noether's theorem for fractional Lagrangian systems invariant under a symmetry group both in the continuous and discrete cases. This provides an explicit conservation law (first integral) given by a closed formula…
Noether's theorem is widely regarded as one of the most elegant results in theoretical physics. The article presents two simple examples that can be used to demonstrate the basic idea behind Noether's theorem, by deriving a relation between…
We propose a unified framework for random locations exhibiting some probabilistic symmetries such as stationarity, self-similarity, etc. A theorem of Noether's type is proved, which gives rise to a conservation law describing the change of…
Internal global symmetries exist for the free non-relativistic Schr\"{o}dinger particle, whose associated Noether charges--the space integrals of the wavefunction and the wavefunction multiplied by the spatial coordinate--are exhibited.…
Noether's theorem, which connects continuous symmetries to exact conservation laws, remains one of the most fundamental principles in physics and dynamical systems. In this work, we draw a conceptual parallel between two paradigms: the…
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…
Non-autonomous non-relativistic mechanics is formulated as Lagrangian and Hamiltonian theory on fibre bundles over the time axis R. Hamiltonian mechanics herewith can be reformulated as particular Lagrangian theory on a momentum phase…
Noether's theorem on the equivalence of symmetry and conservation laws has applications to geometric problems on symmetric spaces. We remind the reader of the theorem and give an application to a variational problem on hyperbolic surfaces.
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…
A simple proof of Noether's first theorem involves the promotion of a constant symmetry parameter $\epsilon$ to an arbitrary function of time, the Noether charge $Q$ is then the coefficient of $\dot\epsilon$ in the variation of the action.…
In this paper we are going to prove a very general fixed point theorem for mappings acting in partial metric spaces. In that theorem we impose some conditions on behavior of considered mappings on orbits and a condition relating orbits 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…
This paper provides a canonical construction of a Noetherian least fixed point topology. While such least fixed point are not Noetherian in general, we prove that under a mild assumption, one can use a topological minimal bad sequence…