Spinors in non-relativistic Chern-Simons electrodynamics

Details Spinors in non-relativistic Chern-Simons electrodynamics Spinors in non-relativistic Chern-Simons electrodynamics

1995-10-17

arxiv.org/abs/hep-th/9510114v1

Annals Phys. 249 (1996) 265-297

Physics

High Energy Physics

High Energy Physics - Theory

Plain TEX, 43 pages

Scientific paper

10.1006/aphy.1996.0071

It is shown that the non-relativistic `Dirac' equation of L\'evy-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 Schr\"odinger symmetric. A spinor representation of the Schr\"odinger 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.

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