Supersymmetry of the planar Dirac - Deser-Jackiw-Templeton system, and of its non-relativistic limit

Abstract

The planar Dirac and the topologically massive vector gauge fields are unified into a supermultiplet involving no auxiliary fields. The superPoincar\'e symmetry emerges from the $osp(1|2)$ supersymmetry realized in terms of the deformed Heisenberg algebra underlying the construction. The non-relativistic limit yields spin 1/2 as well as new, spin 1 "L\'evy-Leblond-type" equations which, together, carry an N=2 superSchr\"odinger symmetry. Part of the latter has its origin in the universal enveloping algebra of the superPoincar\'e algebra.