  The quantum effective action yields equations of motion and correlation
functions including all quantum corrections. We discuss here how it encodes
also Noether currents at the full quantum level. This holds both for
covariantly conserved currents associated to real symmetries that leave the
action invariant as well as for non-conserved Noether currents associated to
extended symmetry transformations which change the action, but in a specific
way. We discuss then in particular symmetries and extended symmetries
associated to space-time geometry for relativistic quantum field theories.
These encompass local dilatations or Weyl gauge transformation, local Lorentz
transformations and local shear transformations. Together they constitute the
symmetry group of the frame bundle GL$(d)$. The corresponding non-conserved
Noether currents are the dilatation or Weyl current, the spin current and the
shear current for which divergence-type equations of motion are obtained from
the quantum effective action.
