Related papers: The Noether Theorems and their Application to Vari…

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…

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…

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…

An infinite sequence of commuting nonpolynomial contact symmetries of the two-dimensional minimal surface equation is constructed. Local and nonlocal conservation laws for $n$-dimensional minimal area surface equation are obtained by using…

We review the {\it Noether Symmetry Approach} as a geometric criterion to select theories of gravity. Specifically, we deal with Noether Symmetries to solve the field equations of given gravity theories. The method allows to find out exact…

In our previous paper, the concept of sub-symmetry of a differential system was introduced, and its properties and some applications were studied. It was shown that sub-symmetries are important in decoupling a differential system, and in…

We derive the Lie and the Noether conditions for the equations of motion of a dynamical system in a $n-$dimensional Riemannian space. We solve these conditions in the sense that we express the symmetry generating vectors in terms of the…

We examine the assumptions behind Noether's theorem connecting symmetries and conservation laws. To compare classical and quantum versions of this theorem, we take an algebraic approach. In both classical and quantum mechanics, observables…

We consider a general theory of all possible quadratic, first-order derivative terms of the non-metricity tensor in the framework of Symmetric Teleparallel Geometry. We apply the Noether Symmetry Approach to classify those models that are…

Hyperbolic conservation laws posed on manifolds arise in many applications to geophysical flows and general relativity. Recent work by the author and his collaborators attempts to set the foundations for a study of weak solutions defined on…

Consideration of the Noether variational problem for any theory whose action is invariant under global and/or local gauge transformations leads to three distinct theorems. These include the familiar Noether theorem, but also two equally…

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…

We summarize the use of Noether symmetries in Minisuperspace Quantum Cosmology. In particular, we consider minisuperspace models, showing that the existence of conserved quantities gives selection rules that allow to recover classical…

We discuss the relation between symmetries and conservation laws in the realm of classical field theories based on the Hamiltonian constraint. In this approach, spacetime positions and field values are treated on equal footing, and a…

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…

A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the…

Emmy Noether proved two deep theorems, and their converses, on the connection between symmetries and conservation laws. Because these theorems are not in the mainstream of her scholarly work, which was the development of modern abstract…

We show that for any variational symmetry of the problem of the calculus of variations on time scales there exists a conserved quantity along the respective Euler-Lagrange extremals.

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

We sketch the main features of the Noether Symmetry Approach, a method to reduce and solve dynamics of physical systems by selecting Noether symmetries, which correspond to conserved quantities. Specifically, we take into account the…