Abstract
It is shown that the non-relativistic “Dirac” equation of Lévy-Leblond, we used recently to describe a spin 12 field interacting non-relativistically with a Chern–Simons gauge field, can be obtained by lightlike reduction from 3+1 dimensions. This allows us to prove that the system is Schrödinger symmetric. A spinor representation of the Schrödinger group is presented. Static, self-dual solutions, describing spinor vortices are given and shown to be the non-relativistic limits of the fermionic vortices found by Choet al. The construction is extended to external harmonic and uniform magnetic fields.
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