Related papers: Noether's 1st theorem with local symmetries
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…
We consider systems of local variational problems defining non vanishing cohomolgy classes. In particular, we prove that the conserved current associated with a generalized symmetry, assumed to be also a symmetry of the variation of the…
The first and second Noether theorems are formulated in a general case of reducible degenerate Grassmann-graded Lagrangian theory of even and odd variables on graded bundles. Such Lagrangian theory is characterized by a hierarchy of…
Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They…
We derive conservation laws in Symmetric Teleparallel Equivalent of General Relativity (STEGR) with direct application of Noether's theorem. This approach allows us to construct covariant conserved currents, corresponding superpotentials…
A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational…
We develop a general approach, based on the Lagrange-Noether machinery, to the definition of invariant conserved currents for gravity theories with general coordinate and local Lorentz symmetries. In this framework, every vector field \xi…
We present a general algorithm constructing a discretization of a classical field theory from a Lagrangian. We prove a new discrete Noether theorem relating symmetries to conservation laws and an energy conservation theorem not based on any…
Noether symmetry of F(R) theory of gravity in vacuum and in the presence of pressureless dust yields F(R) \propto R^{3/2} along with the conserved current \frac{d}{dt}(a\sqrt R) in Robertson-Walker metric and nothing else. Still some…
We show that generalized symmetries cannot be charged under a continuous global symmetry having a Noether current. Further, only non-compact generalized symmetries can be charged under a continuous global symmetry. These results follow from…
In some of the physically interesting gauge systems, we show that the application of the Noether theorem does not lead to the deduction of the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST charges that obey precisely the off-shell…
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 propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a…
An off-shell generalization of the Abbott-Deser-Tekin (ADT) conserved charge was recently proposed by Kim et al. They achieved this by introducing off-shell Noether currents and potentials. In this paper, we construct the crucial off-shell…
The relation between symmetries and local conservation laws, known as Noether's theorem, plays an important role in modern theoretical physics. As a discrete analog of the differentiable physical system, a good numerical scheme should admit…
In this paper, we make a close comparison of a covariant definition of an energy/entropy in general relativity, recently proposed by a collaboration including the present authors, with existing definitions of energies such as the one from…
We study a subclass of Horndeski gravity which has both global conformal and shift symmetries. Global symmetries are characterised by the presence of a conserved current which has been shown to be of particular importance for the…
By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These charges are located at codimension-2 entangling surfaces called…
We provide a proof of the BRST Noether 1.5th theorem, conjectured in [JHEP 10 (2024) 055], for a broad class of rank-1 BV theories including supergravity and 2-form gauge theories. The theorem asserts that the BRST Noether current of any…
Conservation laws of a class of time-dependent damped nonlinear multidimensional wave equations are derived by Noether's theorem. For arbitrary nonzero damping coefficient and nonlinear interaction term, its infinitesimal variational…