相关论文: Noether's theorem in classical mechanics revisited

The invariance theorems obtained in analytical mechanics and derived from Noether's theorems can be adapted to fluid mechanics. For this purpose, it is useful to give a functional representation of the fluid motion and to interpret the…

The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…

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…

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…

Noether's theorem has gained outstanding importance in theoretical particle physics, because it leads to basic conservation laws, such as the conservation of momentum and of angular momentum. Closely related to this theorem, but unnoticed…

We review the Lagrangian formulation of Noether symmetries (as well as "generalized Noether symmetries") in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called "Natural Theories" and "Gauge-Natural…

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…

Being quantized, conserved Noether symmetry functions are represented by Hermitian operators in the space of solutions of the Schrodinger equation, and their mean values are conserved.

Noether's theorem on the equivalence of symmetry and conservation laws has applications to geometric problems on symmetric spaces. We remind the reader of the theorem and give an application to a variational problem on hyperbolic surfaces.

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…

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…

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…

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…

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…

In a series of previous articles by the author, it was shown that one could effectively give a variational formulation to non-conservative mechanical systems, as well as ones that subject to non-holonomic constraints by starting with 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…

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…

This work extends the Ibragimov's conservation theorem for partial differential equations [{\it J. Math. Anal. Appl. 333 (2007 311-328}] to under determined systems of differential equations. The concepts of adjoint equation and formal…

The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class…

We explicate some epistemological implications of stationary principles and in particular of Noether Theorems. Noether's contribution to the problem of covariance, in fact, is epistemologically relevant, since it moves the attention from…