It is shown that the non-relativistic "Dirac" equation of Lévy-Leblond, we used recently to describe a spin 1/2 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 Cho et al. The construction is extended to external harmonic and uniform magnetic fields.
ASJC Scopus subject areas
- Physics and Astronomy(all)