Related papers: Noether's Theorems and Gauge Symmetries
Non-autonomous non-relativistic mechanics is formulated as Lagrangian and Hamiltonian theory on fibre bundles over the time axis R. Hamiltonian mechanics herewith can be reformulated as particular Lagrangian theory on a momentum phase…
The Noether procedure carries an inherent ambiguity due to the necessary local extension, no longer a symmetry, of the global symmetry. The gauging should fix the ambiguity once and for all, however, and, for translations, the general…
Based on a general variational principle, Noether's theorem is revisited. It is shown that the so called pseudotensor problem of the gravitational energy-momentum is a result of mis-reading Noether's theorem, and in fact, all the Noether's…
An iterative Noether scheme, advocated by Deser, is used to introduce gauge invariant couplings to nonrelativistic matter with global symmetries related to usual charge conservation and dipole conservation recently discussed in fractonic…
Emmy Noether proved two deep theorems, and their converses, on the connection between symmetries and conservation laws. Because these theorems are not in the mainstream of her scholarly work, which was the development of modern abstract…
This article focuses on three main contributions. Firstly, we provide an in-depth overview of the nonlocal Lagrangian formalism. Secondly, we introduce an extended version of the second Noether's theorem tailored for nonlocal Lagrangians.…
The gauge symmetry is said unfree if the gauge transformation leaves the action functional unchanged provided for the gauge parameters are constrained by the system of partial differential equations. The best known example of this…
Gravitational effective field theories with nondynamical backgrounds explicitly break diffeomorphism and local Lorentz invariance. At the same time, to maintain observer independence the action describing these theories is required to be…
This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is…
We study the properties of a non-abelian gauge theory subjected to a gauge invariant constraint given by the classical equations of motion. The constraint is not imposed by hand, but appears naturally when we study a particular type of…
The quantum effective action yields equations of motion and correlation functions including all quantum corrections. We discuss here how it encodes also Noether currents at the full quantum level. Interestingly, the construction can be…
We review the geometric formulation of the second Noether's theorem in time-dependent mechanics. The commutation relations between the dynamics on the final constraint manifold and the infinitesimal generator of a symmetry are studied. We…
We review the Lagrangian formulation of Noether symmetries (as well as "generalized Noether symmetries") in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called "Natural Theories" and "Gauge-Natural…
A novel inhomogeneous gauge transformation law is proposed for a non-Abelian adjoint two-form in four dimensions. Rules for constructing actions invariant under this are given. The auxiliary vector field which appears in some of these…
The evolution of a generally covariant theory is under-determined. One hundred years ago such dynamics had never before been considered; its ramifications were perplexing, its future important role for all the fundamental interactions under…
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The…
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)],…
Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in…
Local gauge theories are in a complicated relationship with boundaries. Whereas fixing the gauge can often shave off unwanted redundancies, the coupling of different bounded regions requires the use of gauge-variant elements. Therefore,…
We extend Noether's theorem to dynamical optimal control systems being under the action of nonconservative forces. A systematic way of calculating conservation laws for nonconservative optimal control problems is given. As a corollary, the…