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Various subtleties and problems associated with nonrelativistic (NR)reduction of a scalar field theory to the Schroedinger theory are discussed.Contrary to the usual approaches that discuss the mapping among the equationsof motion or the actions, we highlight the mapping among the space timegenerators. Using a null reduction we show the embedding of the conformalgenerators of the Schroedinger theory to that of a complex scalar theory in onehigher dimension. As applications we reveal the conformal symmetry inhydrodynamics and the obtention of NR diffeomorphism symmetry from therelativistic one. A geometrical connection based on Horava-Lifshitz andNewton-Cartan spacetime is discussed.

On the subtelties of nonrelativistic reduction and applications