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

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 $osp(1\mathrm{\mid }2)$ 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.