Orthosymplectic unification of the Galilei group and BRST

The inclusion of BRST generators into the Poincare group in D dimensions is known to lead IOsp[D, 2vertical stroke2]. Similarly, conformal symmetry gets extended into Osp[D+1, 3vertical stroke2]. For the non-relativistic case we find that the Galilei symmetry gets extended, by inclusion of the BRST generators, into an orthosymplectic symmetry possessing Osp[D, 1vertical stroke2] as a subgroup. All such extensions express the possibility of formulating the classical theories in reparametrization invariant ways. They include besides the generators of the initial kinematical symmetry (Poincare, or conformal, or Galilei), the generators of Parisi-Sourlas transformations. The extended symmetries follow directly through BRST quantization. (orig.)