New aspects of conformal symmetry in 3+1 dimensions

It is known since one hundred years, that the conformal group C(1,3) is the space symmetry group of electromagnetism. With the success of Dirac's spinor equation for the description of electron and other leptons, it was also tried to apply C(1,3), but masses introduce a scale to the theory, which is in contradiction to the dilation invariance of C(1,3). To obtain scale invariance, the masses must be related to other phaenomena (like symmetry breaking) or new particles (e.g. dilaton, Higgs). Another approach using conformal symmetry is the introduction of twistors in 4+2 dimensions, the covering space of the linearized conformal group. It will be shown, that by using a conformal spinor, a conform invariant Lagrangean can be constructed without external fields, including a conventional mass term. With respect to Lorentz-Transformations, this spinor behaves like a Dirac spinor, but dilation, translation and special conformal transformations induce differences. The coupling to gauge bosons is not affected and can be included into the theory just the same way as in Dirac theory. The conformal transformation symmetry can be broken by a simple transformation, which leads to left handed Dirac particle, but with a chiral mass component.