We investigate the symmetry properties for Baym’s Φ-derivable schemes. We show that in general the solutions of the dynamical equations of motion, derived from approximations of the Φ-functional, do not fulfill the Ward-Takahashi identities of the symmetry of the underlying classical action, although the conservation laws for the expectation values of the corresponding Noether currents are fulf...

We revisit the issue that Noether current associated with a local scale symmetry, or equivalently Weyl identically vanishes. Based on only second theorem for we prove symmetry is in general vanishing any invariant gravitational theories four-dimensional Riemannian geometry. also clarify reason: The transformation nondynamical sense it does not contain derivative term of parameter as opposed to ...

It is well-known that all 2d models of gravity—including theories with nonvanishing torsion and dilaton theories—can be solved exactly, if matter interactions are absent. An absolutely (in space and time) conserved quantity determines the global classification of all (classical) solutions. For the special case of spherically reduced Einstein gravity it coincides with the mass in the Schwarzschi...

Properties of Hamiltonian symmetry flows on hyperbolic Euler-type equations are analyzed. Their Lagrangian densities are demonstrated to supply the Hamiltonian operators for subalgebras of their Noether symmetries, while substitutions between Euler-type equations define Miura transformations between the symmetry flows; some Miura maps for Liouvillean Euler-type systems are supplied by their int...