Related papers: Lie, Noether, Kosmann, and Diffeomorphism Anomalie…

It is shown that using Noether's Theorem explicitly employing gauge invariance for variations of the electromagnetic four-potential $A^\mu$ straightforwardly ensures that the resulting electromagnetic energy-momentum tensor is symmetric.…

Noether and Lie symmetry analyses based on point transformations that depend on time and spatial coordinates will be reviewed for a general class of time-dependent Hamiltonian systems. The resulting symmetries are expressed in the form of…

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,…

Through symmetry of the action under global spacetime translations, Noether's first theorem infamously entails an energy-momentum tensor (EMT) that is neither symmetric nor gauge-invariant. In a prior work [Phys. Rev. D 106, 125012 (2022)],…

When discussing consequences of symmetries of dynamical systems based on Noether's first theorem, most standard textbooks on classical or quantum mechanics present a conclusion stating that a global continuous Lie symmetry implies the…

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 exploit an ambiguity somewhat hidden in Noether's theorem to derive systematically, for relativistic field theories, the stress-energy tensor's improvement terms that are associated with additional spacetime symmetries beyond…

We derive the variational principle and Noether's theorem in generally covariant field theory in an explicitly coordinate-independent way by means of the exterior calculus over the space-time manifold. We then focus on the symmetry of…

We derive the Lie and the Noether conditions for the equations of motion of a dynamical system in a $n-$dimensional Riemannian space. We solve these conditions in the sense that we express the symmetry generating vectors in terms of the…

Consideration of the Noether variational problem for any theory whose action is invariant under global and/or local gauge transformations leads to three distinct theorems. These include the familiar Noether theorem, but also two equally…

We prove two general theorems which determine the Lie and the Noether point symmetries for the equations of motion of a dynamical system which moves in a general Riemannian space under the action of a time dependent potential…

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…

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…

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…

Multiple methods for deriving the energy-momentum tensor for a physical theory exist in the literature. The most common methods are to use Noether's first theorem with the 4-parameter Poincar\'{e} translation, or to write the action in a…

New symmetry theorems are obtained for field theories formulated in Minkowski spacetime, based on the recognition that such theories should be diffeomorphism invariant. These theorems, which are in fact generalized Noether theorems, have…

We consider a general theory of all possible quadratic, first-order derivative terms of the non-metricity tensor in the framework of Symmetric Teleparallel Geometry. We apply the Noether Symmetry Approach to classify those models that are…

For a field theory that is invariant under diffeomorphisms there is a subtle interplay between symmetries, conservation laws and the phase space of the theory. The natural language for describing these ideas is that of differential forms…

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…

The hole argument of general relativity threatens a radical and pernicious form of indeterminism. One natural response to the argument is that points belonging to different but isometric models should always be identified, or…