Related papers: Noether's Second Theorem on natural bundles
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 extend Noether's theorem to dynamical optimal control systems being under the action of nonconservative forces. A systematic way of calculating conservation laws for nonconservative optimal control problems is given. As a corollary, 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…
We prove a Noether-Deuring theorem for the derived category of bounded complexes of modules over a Noetherian algebra.
I exhibit the conflicting roles of Noether's two great theorems in defining conserved quantities, especially Energy in General Relativity and its extensions: It is the breaking of coordinate invariance through boundary conditions that…
A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)
Noether's theorem is a fundamental result in physics stating that every symmetry of the dynamics implies a conservation law. It is, however, deficient in several respects: (i) it is not applicable to dynamics wherein the system interacts…
We prove a time scales version of the Noether's theorem relating group of symmetries and conservation laws. Our result extends the continuous version of the Noether's theorem as well as the discrete one and corrects a previous statement of…
We propose an interpretation of the Newton's second law that is suggested by Galilean Relativity theory.
This is the second paper of a series. It extends the results of the first paper from number fields to finitely generated fields, based on the recent theory of adelic line bundles of the same authors. We prove an arithmetic Hodge index…
A generic degenerate Lagrangian system of even and odd variables on an arbitrary smooth manifold is examined in terms of the Grassmann-graded variational bicomplex. Its Euler-Lagrange operator obeys Noether identities which need not be…
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 is reviewed with a particular focus on an intermediate step between global and local gauge and coordinate transformations, namely linear transformations. We rederive the well known result that global symmetry leads to…
The BRST Noether theorem, or ``Noether's 1.5 theorem'', asserts the triviality of the BRST Noether current. We provide two proofs of this theorem that are both valid without restriction on the structure of the gauge theory, extending…
We give an elementary proof of Noether's first Theorem while stressing the magical fact that the global quasi-symmetry only needs to hold for one fixed integration region. We provide sufficient conditions for gauging a global…
In this work we investigate the existence of solutions, their uniqueness and finally dependence on parameters for solutions of second order neutral nonlinear difference equations. The main tool which we apply is Darbo fixed point theorem.
The connection between the Equivalence Principle and Noether's theorem was discussed in S. Capozziello and C. Ferrara, Int. J. Geom. Meth. Mod. Phys. 21, 2440014 (2024). However, it is known that the Noether symmetry condition is…
We extend Furstenberg's structure theorem to any standard Borel $G$-space, where $G$ is any locally compact second countable Noetherian module over a syndetic ring.
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,…
We show that an analogue of the Ball-Box Theorem for step 2, completely non-integrable bundles from smooth sub-Riemannian geometry hold true for a class of non-differentiable tangent subbundles that satisfy a geometric condition. In the…