Related papers: Noether-Like Theorems for Causal Variational Princ…
To what extent does Noether's principle apply to quantum channels? Here, we quantify the degree to which imposing a symmetry constraint on quantum channels implies a conservation law, and show that this relates to physically impossible…
The conservation laws of electromagnetism, and implicitly all theories built from quadratic Lagrangians, are extended to a continuum of nonlocal versions. These are associated with symmetries of a class of equal time field correlation…
In Ref.~\cite{Sag} we proposed a geometric formulation of generalized Nambu mechanics. In the present paper we extend the class of Nambu systems by replacing the stringent condition of constancy of 3-form by closedness. We also explore the…
A lattice Maxwell system is developed with gauge-symmetry, symplectic structure and discrete space-time symmetry. Noether's theorem for Lie group symmetries is generalized to discrete symmetries for the lattice Maxwell system. As a result,…
In this work we prove a weak Noether type theorem for a class of variational problems which include broken extremals. We then use this result to prove discrete Noether type conservation laws for certain classes of finite element…
English version of abstract: The dynamic optimization problems treated by the calculus of variations are usually solved with the help of the 2nd order Euler-Lagrange differential equations. These equations are, generally speaking,…
Because scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action, they do not lead to conservation laws. Instead, an extension of Noether's theorem reduces the equations of motion to…
We study differential systems for which it is possible to establish a correspondence between symmetries and conservation laws based on Noether identity: quasi-Noether systems. We analyze Noether identity and show that it leads to the same…
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…
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…
Noether's theorem is widely regarded as one of the most elegant results in theoretical physics. The article presents two simple examples that can be used to demonstrate the basic idea behind Noether's theorem, by deriving a relation between…
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…
Electromagnetism contains an infinite dimensional symmetry group of large gauge transformations. This gives rise to an infinite number of conserved quantities called "soft charges" via Noether's theorem. When charged particles scatter, the…
It is well-known that all 2d models of gravity---including theories with nonvanishing torsion and dilaton theories---can be solved exactly, if matter interactions are absent. An absolutely (in space and time) conserved quantity determines…
This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics' grand…
The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general…
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…
A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the…
The solution of time dependent differential equations with neural networks has attracted a lot of attention recently. The central idea is to learn the laws that govern the evolution of the solution from data, which might be polluted with…
There has been strong interest in the fate of relativistic symmetries in some quantum spacetimes, also because of its possible relevance for high-precision experimental tests of relativistic properties. However, the main technical results…