Maximal symmetry groups of quantum relativistic equations

Abstract

The author has used Lie's extended group method to obtain the maximal symmetry groups of the Dirac equation for finite mass spin 1/2 particles and the Weyl equation for zero mass spin 1/2 particles. In both cases the maximal symmetry group is an infinite parameter Lie group having an invariant subgroup also of an infinite number of generators. The corresponding factor group for the Dirac equation is an eleven-parameter Lie group isomorphic to the Weyl group. In the case of the Weyl equation the corresponding factor group is a sixteen-parameter Lie group containing a proper subgroup isomorphic to the conformal group.