Related papers: Hamiltonian Noether theorem for gauge systems and …
We analyze the dynamics of the gravitational field when the covariance is restricted to a synchronous gauge. In the spirit of the Noether theorem, we determine the conservation law associated to the Lagrangian invariance and we outline that…
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…
For a linear non-Hermitian system, I demonstrate that a Hamiltonian can be constructed such that the non-Hermitian equations can be expressed exactly in the form of Hamilton's canonical equations. This is first shown for discrete systems…
This review is dedicated to some modern applications of the remarkable paper written in 1918 by E. Noether. On a single paper, Noether discovered the crucial relation between symmetries and conserved charges as well as the impact of gauge…
We analyze the dynamics of gauge theories and constrained systems in general under small perturbations around a classical solution (background) in both Lagrangian and Hamiltonian formalisms. We prove that a fluctuations theory, described by…
In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable (vector) density is known to generate the so--called {\em conserved Noether currents}. It turns out that along any section of the relevant…
This paper deals with conservation laws for mechanical systems with nonholonomic constraints. It uses a Lagrangian formulation of nonholonomic systems and a Cartan form approach. We present what we believe to be the most general relations…
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…
In some of the physically interesting gauge systems, we show that the application of the Noether theorem does not lead to the deduction of the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST charges that obey precisely the off-shell…
We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the time delay variational setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are proved, covering problems of the calculus of…
We present a general algorithm constructing a discretization of a classical field theory from a Lagrangian. We prove a new discrete Noether theorem relating symmetries to conservation laws and an energy conservation theorem not based on any…
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…
We study Lagrangian systems with a finite number of degrees of freedom that are non-local in time. We obtain an extension of Noether theorem and Noether identities to this kind of Lagrangians. A Hamiltonian formalism is then set up for this…
Noether theorem establishes an interesting connection between symmetries of the action integral and conservation laws of a dynamical system. The aim of the present work is to classify the damped harmonic oscillator problem with respect to…
We extend the second Noether theorem to optimal control problems which are invariant under symmetries depending upon k arbitrary functions of the independent variable and their derivatives up to some order m. As far as we consider a…
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
Using the Gitman-Lyakhovich-Tyutin generalization of the Ostrogradsky method for analyzing singular systems, we consider the Hamiltonian formulation of metric and tetrad gravities in two-dimensional Riemannian spacetime treating them as…
It's well known that Noether symmetries lead to the conservation laws. Conserved quantities are constructed out of generator of the symmetry - invariant Hamiltonian vector field. Considering more general class of vector fields -…
We develop a Hamiltonian formalism suitable to be applied to gauge theories in the presence of Gravitation, and to Gravity itself when considered as a gauge theory. It is based on a nonlinear realization of the Poincar\'e group, taken as…
Noether's Theorem yields conservation laws for a Lagrangian with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation laws.…