Non-Relativistic Conformal and Supersymmetries

Abstract

Non-relativistic conformal (''Schr\"odinger'') symmetry is derived in a Kaluza-Klein type framework. Lightlike reduction of the massless Dirac equation from 5D Minkowski space yields L\'evy-Leblond's non-relativistic equation for a spin 1/2 particle. Combining with the osp(1,1) SUSY found before provides us with a super-Schr\"odinger symmetry.