Related papers: Revisiting Noether's Theorem on constants of motio…
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 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…
We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the scale relativity theory setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are proved, covering problems of the calculus…
We introduce an generalized action functional describing the equations of motion and the variational equations for any Lagrangian system. Using this novel scheme we are able to generalize Noether's theorem in such a way that to any…
Noether's theorem in the realm of point dynamics establishes the correlation of a constant of motion of a Hamilton-Lagrange system with a particular symmetry transformation that preserves the form of the action functional. Although usually…
Invariance theorems in analytical mechanics, such as Noether's theorem, can be adapted to continuum mechanics. For this purpose, it is useful to give a functional representation of the motion and to interpret the groups of invariance with…
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…
We describe a recipe to generate "nonlocal" constants of motion for ODE Lagrangian systems. As a sample application, we recall a nonlocal constant of motion for dissipative mechanical systems, from which we can deduce global existence and…
Since the seminal work of Emmy Noether it is well know that all conservations laws in physics, \textrm{e.g.}, conservation of energy or conservation of momentum, are directly related to the invariance of the action under a family of…
In the present work, we formulate a generalization of the Noether Theorem for action-dependent Lagrangian functions. The Noether's theorem is one of the most important theorems for physics. It is well known that all conservation laws,…
Backgrounds are pervasive in almost every application of general relativity. Here we consider the Lagrangian formulation of general relativity for large perturbations with respect to a curved background spacetime. We show that Noether's…
In the present work, we obtain the constants of motion for isoperimetric variational problems with time delay. We consider a constrained optimization problem where the Lagrangian function defining the functional depends on time delayed…
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.…
Hilbert-Noether theorem states that a current associated to diffeomorphism invariance of a Lagrangian vanishes on shell modulo a divergence of an arbitrary superpotential. Application of the Noether procedure to physical Lagrangians yields,…
We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of motion (in the classical sense) that are valid along the mixed…
We give a recipe to generate "nonlocal" constants of motion for ODE Lagrangian systems and we apply the method to find useful constants of motion for dissipative system, for the Lane-Emden equation, and for the Maxwell-Bloch system with…
Diffeomorphism-induced symmetry transformations and time evolution are distinct operations in generally covariant theories formulated in phase space. Time is not frozen. Diffeomorphism invariants are consequently not necessarily constants…
The Noether-Bessel-Hagen theorem can be considered a natural extension of Noether Theorem to search for symmetries. Here, we develop the approach for dynamical systems introducing the basic foundations of the method. Specifically, we…
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…
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.…