The affine sl 2 Toda model coupled to matter field is treated as a constrained system in the context of Faddeev-Jackiw and the (constrained) symplectic schemes. We recover from this theory either, the sine-Gordon or the massive Thirring model, through a process of Hamiltonian reduction, considering the equivalence of the Noether and topological currrents as a constraint and symmetry breaking of...

A general recipe proposed elsewhere to define, via Noether theorem, the variation of energy for a natural field theory is applied to Einstein-Maxwell theory. The electromagnetic field is analysed in the geometric framework of natural bundles. Einstein-Maxwell theory turns then out to be natural rather than gauge-natural. As a consequence of this assumption a correction termà la Regge-Teitelboim...

Based on the generalized operators, Hamilton equation, Noether symmetry, and perturbation to symmetry are studied. The main contents divided into four parts, every part includes two operators. Firstly, equations within operators established. Secondly, method conserved quantity Thirdly, adiabatic invariant presented. And finally, applications presented illustrate methods results.

In this paper, we use the Hojman symmetry approach to find new $(2+1)$-dimensional $f(R)$ gravity solutions, in comparison Noether approach. special case of vector $X=R$, recover BTZ black hole and generalized obtained by approach, interesting point is that cosmological constant appeared as direct manifestation symmetry.

Dual conservation laws of linear planar elasticity theory have been systematically studied based on stress function formalism. By employing generalized symmetry transformation or Lie–B€acklund transformation, a class of new dual conservation laws in planar elasticity have been discovered based on Noether theorem and its Bessel–Hagen generalization. These dual conservation laws represent variati...

We present a detailed study of quantized noncompact, nonlinear SO(1, N) sigma-models in arbitrary space-time dimensions D ≥ 2, with the focus on issues of spontaneous symmetry breaking of boost and rotation elements of the symmetry group. The models are defined on a lattice both in terms of a transfer matrix and by an appropriately gauge-fixed Euclidean functional integral. The main results in ...

Abstract The Noether symmetry analysis is applied in a multiscalar field cosmological model teleparallel gravity. In particular, we consider two scalar fields with interaction scalar-torsion theory. equations have minisuperspace description, and the evolution of physical variables depends on potential function that drives fields’ dynamics. With requirement for to admit non-trivial point symmetr...