Related papers: Noether's Theorem with Momentum and Energy Terms f…

In the present work, by taking advantage of a so-called practical limitation of fractional derivatives, namely, the absence of a simple chain and Leibniz's rules, we proposed a generalized fractional calculus of variation where the…

Noether symmetry for higher order gravity theory has been explored, with the introduction of an auxiliary variable which gives the only correct quantum desccription of the theory, as shown in a series of earlier papers. The application of…

The macroscopic energy-momentum and spin densities of relativistic spin hydrodynamics are obtained from the ensemble average of their respective microscopic definitions (quantum operators). These microscopic definitions suffer from…

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…

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…

We present an extension of the classical theory of calculus of variations to generalized functions. The framework is the category of generalized smooth functions, which includes Schwartz distributions while sharing many nonlinear properties…

We clarify the relation between canonical and metric energy-momentum tensors. In particular, we show that a natural definition arises from Noether's Theorem which directly leads to a symmetric and gauge invariant tensor for electromagnetic…

Noether's theorem is an elegant and powerful tool of classical mechanics, but it is of little to no consequence in discrete theories. Here we define and explore a discrete approach to covariant mechanics and show that within this framework…

The search for Noether point symmetries for non-relativistic charged particle motion is reduced to the solution for a set of two coupled, linear partial differential equations for the electromagnetic field. These equations are completely…

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…

A description of the motion in noninertial reference frames by means of the inclusion of high time derivatives is studied. Incompleteness of the description of physical reality is a problem of any theory, both in quantum mechanics and…

Hilbert-Noether theorem states that a current associated to diffeomorphism invariance of a Lagrangian vanishes on shell modulo a divergence of an arbitrary superpotential. Application of the Noether procedure to physical Lagrangians yields,…

In this paper we introduce the use of Sylvester's formula for systems with degenerate eigenvalues in relation to obtaining their analytical solutions. To appreciate the use we include two other forms of analytical solutions namely adiabatic…

Lie symmetry analysis is an established method for generating symmetries of differential equations. We apply this method together the generalized fundamental theorem of double reduction. In particular, Noether symmetries and some associated…

We give a new representation as tempered distribution for the energy-momentum tensor of a system of charged point-particles, which is free from divergent self-interactions, manifestly Lorentz-invariant and symmetric, and conserved. We…

We develop a non-anticipating calculus of variations for functionals on a space of laws of continuous semi-martingales, which extends the classical one. We extend Hamilton's least action principle and Noether's theorem to this generalized…

Local symmetry transformations play an important role for establishing the existence and form of a conserved (Noether) current in systems with a global continuous symmetry. We explain how this fact leads to the existence of linear relations…

A general approach is presented for quantizing a metric nonlinear system on a manifold of constant curvature. It makes use of a curvature dependent procedure which relies on determining Noether symmetries from the metric. The curvature of…

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…

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…