On a non-CP-violating electric dipole moment of elementary particles
  A description of elementary particles should be based on irreducible representations of the Poincar\'e group. In the theory of massive representations of the full Poincar\'e group there are essentially four different cases. One of them corresponds to the ordinary Dirac theory. The extension of Dirac theory to the remaining three cases makes it possible to describe an anomalous electric dipole moment of elementary particles without breaking the reflections. 
J. Giesen