Abstract
In this paper two things are done. We first prove that an arbitrary power p of the Schrödinger Lagrangian in arbitrary dimension always enjoys the non-relativistic conformal symmetry. The implementation of this symmetry on the dynamical field involves a phase term as well as a conformal factor that depends on the dimension and on the exponent. This non-relativistic conformal symmetry is shown to have its origin on the conformal isometry of the power p of the Klein–Gordon Lagrangian in one higher dimension which is related to the phase of the complex scalar field.
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