The Noether symmetry of a generic f(R) cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generators of the desired symmetry. We explicitly calculate the form of f(R) for which such symmetries exist. It is shown that the resulting form of f(R) yields a power law expansion for the cosmological scale factor. We also obtain the effe...

The relationship between symmetry fields and first integrals of divergence-free vector is explored in three dimensions light its relevance to plasma physics magnetic confinement fusion. A Noether-type theorem known: for each such symmetry, there corresponds a integral. extent which the converse true investigated. In doing so, reformulation this found holds on what called toroidal region. Some c...

The Noether symmetry of a generic f(R) cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generators of the desired symmetry. We explicitly calculate the form of f(R) for which such symmetries exist. It is shown that the resulting form of f(R) yields a power law expansion for the cosmological scale factor. We also obtain the effe...

A formalism describing the dynamics of classical and quantum systems from a group theoretical point of view is presented. We apply it to the simple example of the classical free particle. The Galileo group G is the symmetry group of the free equations of motion. Consideration of the free particle Lagrangian semi-invariance under G leads to a larger symmetry group, which is a central extension o...

: Singular systems play an important role in many fields, and some new fractional operators, which are general, have been proposed recently. Therefore, singular on the basis of mixed derivatives including integer order derivative generalized operators studied. Firstly, Lagrange equations within established, primary constraints presented for systems. Then constrained Hamilton constructed by intr...

and (F ×G) = fabcF G. Under the assumption that BRS singlets have positive metric, it is proved that Vphys has positive semidefinite in such a way that BRS quartet particles appear only in zero norm. One finds from the BRS transformation that for each colour a, a set of massless asymptotic fields χ, β, γ, γ̄ form a BRS quartet. The Noether current corresponding to the conservation of the colour ...

We show the existence of a co(dual)-BRST symmetry for the usual BRST invariant Lagrangian density of an Abelian gauge theory in two dimensions of space-time where a U(1) gauge field is coupled to the Noether conserved current (constructed by the Dirac fields). Under this new symmetry, it is the gauge-fixing term that remains invariant and the symmetry transformations on the Dirac fields are ana...