Related papers: Extensions of Noether's Second Theorem: from conti…
Using the fact that extremum of variation of generalized action can lead to the fractional dynamics in the case of systems with long-range interaction and long-term memory function, we consider two different applications of the action…
Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and…
An iterative Noether scheme, advocated by Deser, is used to introduce gauge invariant couplings to nonrelativistic matter with global symmetries related to usual charge conservation and dipole conservation recently discussed in fractonic…
As is well known, there are different Lagrangians which lead to the same Euler-Lagrange operator. The gauge invariance of a Lagrangian guarantees that of the corresponding Euler-Lagrange operator, but not vice versa. We show that the gauge…
Two-dimensional gas dynamics equations in mass Lagrangian coordinates are studied in this paper. The equations describing these flows are reduced to two Euler-Lagrange equations. Using group classification and Noether's theorem,…
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 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…
Noether's first and second theorems both imply conserved currents that can be identified as an energy-momentum tensor (EMT). The first theorem identifies the EMT as the conserved current associated with global spacetime translations, while…
We prove a generalization of Noether's theorem for optimal control problems defined on time scales. Particularly, our results can be used for discrete-time, quantum, and continuous-time optimal control problems. The generalization involves…
Noether's first theorem does not establish a one-way explanatory arrow from symmetries to conservation laws, but such an arrow is widely assumed in discussions of the theorem in the physics and philosophy literature. It is argued here that…
The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…
We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…
A fundamental tenet of gauge theory is that physical quantities should be gauge-invariant. This prompts the question: can gauge symmetries have physical significance? On one hand, the Noether theorems relate conserved charges to symmetries,…
General Lagrangian theory of even and odd fields on an arbitrary smooth manifold is considered. Its non-trivial reducible gauge symmetries and their algebra are defined in this very general setting by means of the inverse second Noether…
We lay down a set of requirements for a field theory to produce a covariant conservation law out of Noether's second theorem, and show that neither local invariance implies a covariant conservation law, nor the existence of a covariant…
This paper is devoted to the study of mechanical systems subjected to external forces in the framework of symplectic geometry. We obtain a Noether's theorem for Lagrangian systems with external forces, among other results regarding…
In this paper we study symmetries, Newtonoid vector fields, conservation laws, Noether's Theorem and its converse, in the framework of the $k$-symplectic formalism, using the Fr\"olicher-Nijenhuis formalism on the space of $k^1$-velocities…
The hierarchy of the integrable nonlinear equations associated with the quadratic bundle is considered. The expressions for the solution of the linearization of these equations and their conservation law in the terms of the solutions of the…
This paper provides a modern presentation of Noether's theory in the realm of classical dynamics, with application to the problem of a particle submitted to both a potential and a linear dissipation. After a review of the close…
The paper discusses the mathematical consequences of the application of derived variables in gauge fields. Physics is aware of several phenomena, which depend first of all on velocities (like e.g., the force caused by charges moving in a…