Neother’s theorem on quantum hydrodynamics

This research aims to formulate conserved quantities (classical observables) in Noether’s theorem for quantum hydrodynamics within the framework of symplectic geometry. The symplectic one-form or symplectic potential is identical to the Noether current. 31 The Noether current plays an important role in determining classical observables and conserved quantities, namely, [Formula: see text] and [Formula: see text] associated with the above symmetry in quantum hydrodynamics (nonrelativistic and relativistic) associated with Killing vector field and rotational symmetry group [Formula: see text].