We study, in the framework of the global inverse problem of the calculus of variations, the first order variational problems defined by a family of local Lagrangian densities. We will show that those local variational problems for which the differential of the Poincaré–Cartan form is globally defined, admit a geometrical formulation which apart from some cohomological obstructions is closely re...

Recall the global U(1) symmetry: Ψ→ e−ieΨ i.e. δΨ = −ieΨ. Let’s run the Noether argument: consider a slightly deformed, infinitesimal version of the symmetry transformation: Ψ→ Ψ + ρδΨ, where is just a small number to keep track of order, and ρ is some general function of x. The fact that we have a U(1) symmetry tells us the action must change under the deformed transformation by δS = ∫ dx J N∂...

We quantize a flat FRW cosmology in the context of the f(R) gravity by Noether symmetry approach. We explicitly calculate the form of f(R) for which such symmetries exist. It is shown that the existence of a Noether symmetry yields a general solution of the Wheeler-DeWitt equation where can be expressed as a superposition of states of the form e . In terms of Hartle criterion, this type of wave...

The existence of a Noether symmetry for a given minisuperspace cosmological model is a sort of selection rule to recover classical behaviours in cosmic evolution since oscillatory regimes for the wave function of the universe come out. The so called Hartle criterion to select correlated regions in the configuration space of dynamical variables can be directly connected to the presence of a Noet...

abstract We construct a relativistically covariant symmetry of QED. Previous local and nonlocal symmetries are special cases. This generalized symmetry need not be nilpotent, but nilpotency can be arranged with an auxiliary field and a certain condition. The Noether charge generating the symmetry transformation is obtained, and it imposes a constraint on the physical states.

A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the invariance condition develops as a set of partial differential equations determining the symmetry transformation. The solution is provided in the case of real s...

A new symmetry for Newtonian Dynamics is analyzed, this corresponds to going an accelerated frame, which introduces a constant gravitational field into the system and subsequently. We consider addition of linear contribution potential $$\phi $$ can be used cancel induced by from, combination these two operations produces then symmetry. This leads Noether current conserved. The conserved charges...