Identically conserved currents and their charges

We examine, at a classical level, the features that distinguish dynamically conserved currents from identically conserved ones. Then we prove that, in four spacetime dimensions, the quantum charges corresponding to identically conserved currents always annihilate the vacuum state. We illustrate our discussion with several examples.     

Hidden Yangians in 2D massive current algebras

We define non-local conserved currents in massive current algebras in two dimensions. Our approach is algebraic and non-perturbative. The non-local currents give a quantum field realization of the Yangians. We show how the noncocommutativity of the Yangians is related to the non-locality of the currents. We discuss the implications of the existence of non-local conserved charges on theS-matrices.Laboratoire de la Direction des sciences de la matière du Commissariat à l'énergie atomique     

Conserved currents in the massive thirring model

The existence of an infinite set of conserved currents in the massive Thirring model is discussed. The first four nontrivial currents are given explicitely.     

More Nonlocal Conserved Currents in Chiral Sigma Models

The infinite many nonlocal conserved currents are given for the principal chiral model. Wess-Zuminc-Witten chiral model and the supersymmetric chiral model with respect to the new hidden symmetry transformatione. It is shown that these conserved currents are related to the classical r-matrix and thus decompose into many families. The approach used here provides a systematic method to derive the Casimir operators for the infinite dimensional Lie algebras in its nonunitary and nonhighest weight representations.     

The conserved currents for the Maxwellian field

We classify the conserved currents for the Maxwellian field. There are four families: (1) the classical currents derived using Noether's theorem from conformal invariance (2) certain Noetherian currents based on translations in field space, (3,4) two more kinds not equivalent to any Noetherian form.     

Total conserved charges of Kerr-NUT spacetimes using Poincaré version of teleparallel equivalent of general relativity

Total conserved charges of several axially symmetric tetrad spacetimes generating Kerr-NUT metric are calculated by using the approach of invariant conserved currents. Certain tetrads give the known values, while others give unusual charges and divergent quantities. Therefore, regularized expressions are employed to get the known form of conserved charges.     

Hopf Solitons and Area-Preserving Diffeomorphisms of the Sphere

We consider a (3+1)-dimensional local field theory defined on the sphere S ². The model possesses exact soliton solutions with nontrivial Hopf topological charges and an infinite number of local conserved currents. We show that the Poisson bracket algebra of the corresponding charges is isomorphic to that of the area-preserving diffeomorphisms of the sphere S ². We also show that the conserved currents under consideration are the Noether currents associated to the invariance of the Lagrangian under that infinite group of diffeomorphisms. We indicate possible generalizations of the model.     

Covariantized Nœther identities and conservation laws for perturbations in metric theories of gravity

A construction of conservation laws and conserved quantities for perturbations in arbitrary metric theories of gravity is developed. In an arbitrary field theory, with the use of incorporating an auxiliary metric into the initial Lagrangian covariantized N?ther identities are carried out. Identically conserved currents with corresponding superpotentials are united into a family. Such a generalized formalism of the covariantized identities gives a natural basis for constructing conserved quantities for perturbations. A new family of conserved currents and correspondent superpotentials for perturbations on arbitrary curved backgrounds in metric theories is suggested. The conserved quantities are both of pure canonical N?ther and of Belinfante corrected types. To test the results each of the superpotentials of the family is applied to calculate the mass of the Schwarzschild-anti-de Sitter black hole in the Einstein–Gauss–Bonnet gravity. Using all the superpotentials of the family gives the standard accepted mass.     

NOETHER AND TOPOLOGICAL CHARGE OF GAUGE FIELD

"Electric" chaise currents with gauge-dependent isotopic axis are gauge invariant Noether currents. These currnnts include themselves the contribution of gauge field. "Magrnetic" poles are related to the topologically nontrivial orientation of isotopic axis. The dual symmetry trans-forms a known conserved current into infinitely many ved currents. The induced Noether charges of vacuum different chiral boundary condition and the topological background charges always compensate each other.     

Conserved currents and symmetry transformations in local scattering theory

The relation between conserved currents and symmetries of theS-matrix is investigated within the framework of Wightman field theory. Assuming a complete particle interpretation with no massless particles, it is shown that every conserved current yields a self-adjoint charge operator which acts additively onn-particle states and commutes with theS-matrix. For currents satisfying current algebra relations of a groupG, the corresponding charges generate a unitary representation ofG.     

On the solution of Polyakov's ansatz

I show that the functional differential equations for conserved currents in loop space are consistent with the integrability condition.     

Explicit construction of conserved currents for massless fields of arbitrary spin

We give an explicit construction of conserved currents for massless fields of arbitrary spin. These currents are gauge invariant and conserved on shell. Also they allow for the construction of a large class of trilinear interaction terms for the interaction between a massless spin-s₁ field and two spin-s₂ fields. The class is restricted only to 2s₂⩽s₁. In case s₁ = 4 and s₂ = 2, the current is the linearized Bel-Robinson tensor. To these conserved currents corresponds an infinite dimensional Lie algebra of global infinitesimal invariances of the action of a free massless field of arbitrary spin.     

The Hamilton-Cartan formalism for higher order conserved currents: 1. Regular first order Lagrangians

The Hamilton–Cartan formalism for regular first order Lagrangian field theories is extended to deal with conserved currents which depend on higher order derivatives of the field variables. These conserved currents are characterized. Exterior differential systems I^{(k + 1)} and I equivalent to the k-th and infinite prolongations of the Euler-Lagrange equations are defined. It is shown that to each conserved current is associated an equivalence class of infinitesimal symmetries of I. Conserved charges are defined and a Poisson bracket is constructed by analogy with the usual definition. The sine-Gordon equation is treated briefly as an application of the formalism.     

Nonconservation of gauge singlet charge operators in light cone field theories

A light cone gauge theory is considered which possesses one or more conserved currents. It is shown quite generally that the usual associated charge operator is not conserved whenever the current transforms as a vector in Minkowski space. This includes the case of a conserved current which is a singlet under the operations of any group associated with a coupling to a non-abelian gauge field. As one application of this result one infers that there are no conserved flavor charge operators in the light cone formulation of quantum chromodynamics.     

The Hamilton Cartan formalism for rth-order Lagrangians and the integrability of the KdV and modified KdV equations

The Hamilton Cartan formalism for rth order Lagrangians is presented in a form suited to dealing with higher-order conserved currents. Noether's Theorem and its converse are stated and Poisson brackets are defined for conserved charges. An isomorphism between the Lie algebra of conserved currents and a Lie algebra of infinitesimal symmetries of the Cartan form is established. This isomorphism, together with the commutativity of the Bäcklund transformations for the KdV and modified KdV equations, allows a simple geometric proof that the infinite collections of conserved charges for these equations are in involution with respect to the Poisson bracket determined by their Lagrangians. Thus, the formal complete integrability of these equations appears as a consequence of the properties of their Bäcklund transformations.It is noted that the Hamilton Cartan formalism determines a symplectic structure on the space of functionals determined by conserved charges and that, in the case of the KdV equation, the structure is the same as that given by Miura et al. [5].     

The dynamical differential forms of the Klein—Gordon field

We classify the conserved currents for the Klein-Gordon field. We show that there are many which are not associated with invariances of the Lagrangian.     

Causality properties of form factors

Causality is proven for the known form factors of the one-particle matrix elements of the current commutator. The cases of conserved and non-conserved currents are considered.     

Flat Currents and Solutions of Sigma Model on Supercoset Targets with Z2m Grading

We find one parameter fiat currents of the sigma model on supercoset targets with Z2m grading given by Young satisfaction equations of motion and the Virasoro constraint. This means that one can generate a series of classical solutions from the original one. For these new solutions one can also construct fiat currents and conserved charges, which form the same set with the original one.     

The dynamic differential forms of the Klein-Gordon field and the conformal group

Dynamic differential forms are the natural generalization of conserved currents. We discover the entire class for the real Klein-Gordon field, and find that each dynamic form is equivalent to a Noetherian form, that is, a form based on a canonical symmetry. Going to the complex case, we classify also its dynamic currents. It appears that some of them are definitely not equivalent to Noetherian forms.