Related papers: Symmetries of line bundles and Noether theorem for…
We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincar\'e-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincar\'e-Cartan form is…
The time dependent-integrals of motion, linear in position and momentum operators, of a quantum system are extracted from Noether's theorem prescription by means of special time-dependent variations of coordinates. For the stationary case…
Noether and Lie symmetry analyses based on point transformations that depend on time and spatial coordinates will be reviewed for a general class of time-dependent Hamiltonian systems. The resulting symmetries are expressed in the form of…
The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the…
Conservation laws of a class of time-dependent damped nonlinear multidimensional wave equations are derived by Noether's theorem. For arbitrary nonzero damping coefficient and nonlinear interaction term, its infinitesimal variational…
The recently-developed techniques of Noether analysis of the quantum-group spacetime symmetries of some noncommutative field theories rely on the {\it ad hoc} introduction of some peculiar auxiliary transformation parameters, which appear…
The search for Noether point symmetries for non-relativistic charged particle motion is reduced to the solution for a set of two coupled, linear partial differential equations for the electromagnetic field. These equations are completely…
We prove two general theorems which determine the Lie and the Noether point symmetries for the equations of motion of a dynamical system which moves in a general Riemannian space under the action of a time dependent potential…
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…
There exist instances of dynamical systems possessing symmetry transformations of which the conserved Noether charges generating these symmetries feature an explicit time dependence in their functional representation over phase space. The…
The infinite number of time-dependent linear in field and conjugated momenta invariants is derived for the scalar field using the Noether's theorem procedure.
We find the Noether point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries are composed of a quasi-invariance transformation, a time-dependent rotation and a time-dependent spatial translation. The…
In contact Hamiltonian systems, the so-called dissipated quantities are akin to conserved quantities in classical Hamiltonian systems. In this paper, we prove a Noether's theorem for non-autonomous contact Hamiltonian systems,…
We review the geometric formulation of the second Noether's theorem in time-dependent mechanics. The commutation relations between the dynamics on the final constraint manifold and the infinitesimal generator of a symmetry are studied. We…
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…
In Ref.~\cite{Sag} we proposed a geometric formulation of generalized Nambu mechanics. In the present paper we extend the class of Nambu systems by replacing the stringent condition of constancy of 3-form by closedness. We also explore the…
Noether's theorem connects symmetries to invariants in continuous systems, however its extension to discrete systems has remained elusive. Recognizing the lowest-order finite difference as the foundation of local continuity, a viable method…
Noether invariance in statistical mechanics provides fundamental connections between the symmetries of a physical system and its conservation laws and sum rules. The latter are exact identities that involve statistically averaged forces and…
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 consider a class of non-linear PDE systems, whose equations possess Noether identities (the equations are redundant), including non-variational systems (not coming from Lagrangian field theories), where Noether identities and…