It is shown that the Lie algebra of Noether symmetries for the Lagrangian minimizing an n − 1 area enclosing a constant n-volume in a Euclidean space is so n ⊕sR and in a space of constant curvature the Lie algebra is so n . Furthermore, if the space has one section of constant curvature of dimension n1, another of n2, and so on to nk and one of zero curvature of dimension m, with n ≥ ∑kj 1 nj ...

We show that the basic results on the paper referred in the title [J. Phys. A: Math. Gen. 35 (2002) 5333-5345], concerning the derivation of the Ermakov invariant from Noether symmetry methods, are not new. PACS numbers: 02.30.Hg, 02.90.+p, 03.20.+i The purpose of this comment is to point out that the main results presented in a recently published paper [1], are not new. At the end of the intro...

Higher–order corrections of Einstein–Hilbert action of general relativity can be recovered by imposing the existence of a Noether symmetry to a class of theories of gravity where Ricci scalar R and its d’Alembertian 2R are present. In several cases, it is possible to get exact cosmological solutions or, at least, to simplify dynamics by recovering constants of motion. The main result is that a ...

Dynamical breaking of chiral symmetry in effective models of QCD is studied. Introducing a cut-off function or a non-local interaction, the Noether current must be modified and thus the Ward–Takahashi identity and the PCAC relation are modified accordingly. We point out that the pion decay constant must be defined consistently with the Noether current so that the low-energy relations are satisf...