Internal-Symmetry Groups and Their Automorphisms

Abstract

It is proposed that outer automorphisms of degenerate internal-symmetry groups must be symmetry operators themselves. In general, however, they are hidden (spontaneously broken) symmetries. Consequences of this proposition are studied. It is found that internal-symmetry groups are not arbitrary but that their intrinsic properties play an important role. The existence of discrete symmetries (such as charge conjugation) follows naturally from assuming the continuous symmetry groups (such as gauge groups). We also find that the enlargement of the isospin symmetry and parity leads directly to the chiral SU(3) \ifmmode\times\else\texttimes\fi{} SU(3), so that the existence of an "exact SU(3) limit" is in principle not allowed.