Symmetrieeigenschaften achtkomponentiger Spinorfelder im Gitterraum

Starting from the four component Dirac equation for free particles without mass W.Heisenberg und W.Pauli have shown that the interaction term is uniquely defined, if one requires that all symmetries of free particles are preserved. Here we obtain similar results if we start from the eight component Dirac equation for free particles without mass:

1. The symmetry group of the eight component Dirac equation for free particles without mass has 16 parameters. It is isomorph to the direct product of the SU 4 and a one-parametric group: SU 4× (1).
2. The interaction operator is uniquely defined if one requires to preserve as many symmetries as possible of those given in (1).
3. But some of the symmetries in (1) are necessarily broken, in particular that of SU 3. The symmetry of the interaction operator is given by SO 4× (1)× (1).

These results mean:

1. The Heisenberg theory is uniquely defined, only if one assumes that the free particle part of the equation is well known.
2. The theory can be changed without modifying the fundamental idea ofHeisenberg andPauli to deduce an uniquely defined interaction operator if one starts with a modified free particle part.
3. A special kind of modification of the free particle part leads essentially to the SU 4-symmetry including that of SU 3, which is necessarily broken by the interaction term.
4. The question arises if this break of the SU 3-symmetry has something to do with the real break. This question is not yet touched in this paper.