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Conformal symmetry of an extended Schrödinger equation and its relativistic origin.(English)Zbl 1115.81040

Summary: 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.

MSC:

81R20 Covariant wave equations in quantum theory, relativistic quantum mechanics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics

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