Related papers: A Noether Theorem for discrete Covariant Mechanics
The energy-momentum conservation laws for general reduced-fluid (e.g., gyrofluid) models are derived by Noether method from a general reduced variational principle. The reduced canonical energy-momentum tensor (which is explicitly…
This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fundamental geometric structures as well as their preservation…
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…
All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted…
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…
We give a version of Noether theorem adapted to the framework of mu-symmetries; this extends to such case recent work by Muriel, Romero and Olver in the framework of lambda-symmetries, and connects mu-symmetries of a Lagrangian to a…
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…
Relying on known results of the Noether theory of symmetries extended to constrained systems, it is shown that there exists an obstruction that prevents certain tangent-space diffeomorphisms to be projectable to phase-space, for generally…
Noether's theorems are widely praised as some of the most beautiful and useful results in physics. However, if one reads the majority of standard texts and literature on the application of Noether's first theorem to field theory, one…
We develop the general theory of Noether symmetries for constrained systems. In our derivation, the Dirac bracket structure with respect to the primary constraints appears naturally and plays an important role in the characterization of the…
We present a variational approach for relativistic ideal hydrodynamics interacting with electromagnetic fields. The momentum of fluid is introduced as the canonical conjugate variable of the position of a fluid element, which coincides with…
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…
There exist instances of dynamical systems possessing symmetry transformations of which the conserved Noether charges generating these symmetries feature an explicit time dependence in their functional representation over phase space. The…
I shall sketch the contents of Noether's 1918 article, "Invariante Variationsprobleme", in the context of the debate on the conservation of energy that had arisen from Einstein's general theory of relativity. How original was Noether's…
We consider the continuous and discrete-time Hamilton's variational principle on phase space, and characterize the exact discrete Hamiltonian which provides an exact correspondence between discrete and continuous Hamiltonian mechanics. The…
Using the recent formulation of Noether's theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler-Lagrange equations, we prove a Noether-like theorem to…
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…
This review is dedicated to some modern applications of the remarkable paper written in 1918 by E. Noether. On a single paper, Noether discovered the crucial relation between symmetries and conserved charges as well as the impact of gauge…
Noether invariance in statistical mechanics provides fundamental connections between the symmetries of a physical system and its conservation laws and sum rules. The latter are exact identities that involve statistically averaged forces and…
We introduce a method to construct conservation laws for a large class of linear partial differential equations. In contrast to the classical result of Noether, the conserved currents are generated by any symmetry of the operator, including…