Duality Induced Reflections and CPT

Abstract

The linear particle-antiparticle conjugation $\ty C$ and position space reflection $\ty P$ as well as the antilinear time reflection $\ty T$ are shown to be inducable by the selfduality of representations for the operation groups $\SU(2)$, $\SL(\C^2)$ and $\R$ for spin, Lorentz transformations and time translations resp. The definition of a colour compatible linear $\ty{CP}$-reflection for quarks as selfduality induced is impossible since triplet and antitriplet $\SU(3)$-representations are not linearly equivalent.