相关论文: Noether's theorem for the variational equations

This paper presents a formulation of Noether's theorem for fractional classical fields. We extend the variational formulations for fractional discrete systems to fractional field systems. By applying the variational principle to a…

In Noether's original presentation of her celebrated theorm of 1918 allowance was made for the dependence of the coefficient functions of the differential operator which generated the infinitesimal transformation of the Action Integral upon…

Noether's theorem relates constants of motion to the symmetries of the system. Here we investigate a manifestation of Noether's theorem in non-Hermitian systems, where the inner product is defined differently from quantum mechanics. In this…

A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational…

We consider the problem of a conditional extremum of an action in a class of fields constrained by differential equations. For this setup, we propose an extension of Noether's first theorem to connect the symmetries of the action and the…

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…

We prove a fractional Noether's theorem for fractional Lagrangian systems invariant under a symmetry group both in the continuous and discrete cases. This provides an explicit conservation law (first integral) given by a closed formula…

The recently discovered conserved quantity associated with Kepler rescaling is generalised by an extension of Noether's theorem which involves the classical action integral as an additional term. For a free particle the familiar…

Here we consider scale invariant dynamical systems within a classical particle description of Lagrangian mechanics. We begin by showing the condition under which a spatial and temporal scale transformation of such a system can lead to a…

Making use of the Lagrange anchor construction introduced earlier to quantize non-Lagrangian field theories, we extend the Noether theorem beyond the class of variational dynamics.

We consider the Lagrangian formulation with duplicated variables of dissipative mechanical systems. The application of Noether theorem leads to physical observable quantities which are not conserved, like energy and angular momentum, and…

We prove a DuBois-Reymond necessary optimality condition and a Noether symmetry theorem to the recent quantum variational calculus of Cresson. The results are valid for problems of the calculus of variations with functionals defined on sets…

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…

We prove multidimensional integration by parts formulas for generalized fractional derivatives and integrals. The new results allow us to obtain optimality conditions for multidimensional fractional variational problems with Lagrangians…

We prove Noether-type theorems for fractional isoperimetric variational problems with Riemann-Liouville derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples, in the fractional context of the calculus…

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 derive the variational principle and Noether's theorem in generally covariant field theory in an explicitly coordinate-independent way by means of the exterior calculus over the space-time manifold. We then focus on the symmetry of…

Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…

We introduce a variational setting for the action functional of an autonomous and indefinite Lagrangian on a finite dimensional manifold. Our basic assumption is the existence of an infinitesimal symmetry whose Noether charge is the sum of…

In this paper we revisit Noether's theorem on the constants of motion for Lagrangian mechanical systems in the ODE case, with some new perspectives on both the theoretical and the applied side. We make full use of invariance up to a…