Related papers: The Noether Theorems and their Application to Vari…
The relation between symmetries and local conservation laws, known as Noether's theorem, plays an important role in modern theoretical physics. As a discrete analog of the differentiable physical system, a good numerical scheme should admit…
A geometric framework, called multicontact geometry, has recently been developed to study action-dependent field theories. In this work, we use this framework to analyze symmetries in action-dependent Lagrangian and Hamiltonian field…
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…
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 extend Noether's theorem to dynamical optimal control systems being under the action of nonconservative forces. A systematic way of calculating conservation laws for nonconservative optimal control problems is given. As a corollary, the…
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.
We study Noether symmetries in two-field cosmological $\alpha$-attractors, investigating the case when the scalar manifold is an elementary hyperbolic surface. This encompasses and generalizes the case of the Poincare disk. We solve the…
We develop a systematic algorithm, based on Noether's theorem, for defining the various currents in theories invariant under space dependent polynomial symmetries. A master equation is given that yields all the conservation laws…
In this paper we study symmetries, Newtonoid vector fields, conservation laws, Noether's Theorem and its converse, in the framework of the $k$-symplectic formalism, using the Fr\"olicher-Nijenhuis formalism on the space of $k^1$-velocities…
We discuss geometric properties of non-Noether symmetries and their possible applications in integrable Hamiltonian systems. Correspondence between non-Noether symmetries and conservation laws is revisited. It is shown that in regular…
This work provides a general overview for the treatment of symmetries in classical field theories and (pre)multisymplectic geometry. The geometric characteristics of the relation between how symmetries are interpreted in theoretical physics…
We prove that under certain assumptions a partial differential equation can be derived from a variational principle. It is well-known from Noether's theorem that symmetries of a variational functional lead to conservation laws of the…
Regular perturbative Lagrangians that admit approximate Noether symmetries and approximate conservation laws are studied. Specifically, we investigate the connection between approximate Noether symmetries and collineations of the underlying…
We derive the Noether identities and the conservation laws for general gravitational models with arbitrarily interacting matter and gravitational fields. These conservation laws are used for the construction of the covariant equations of…
The aim of this note is to discuss the relation between one-parameter continuous symmetries of the dynamics, defined on physical grounds, and conservation laws. In the Hamiltonian formulation, such symmetries of the dynamics in general…
Noether's calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather consider generating functionals, such as the…
We give a version of Noether theorem adapted to the framework of mu-symmetries; this extends to such case recent work by Muriel, Romero and Olver in the framework of lambda-symmetries, and connects mu-symmetries of a Lagrangian to a…
We apply the Noether Symmetry Approach to point-like teleparallel Lagrangians in view to derive minisuperspaces suitable for Quantum Cosmology. Adopting the Arnowitt-Deser-Misner formalism, we find out related Wave Functions of the…
We consider Noether symmetries of the equations defined by the sections of characteristic line bundles of nondegenerate 1-forms and of the associated perturbed systems. It appears that this framework can be used for time-dependent systems…
The direct method based on the definition of conserved currents of a system of differential equations is applied to compute the space of conservation laws of the (1+1)-dimensional wave equation in the light-cone coordinates. Then Noether's…