Space-Time Properties and Internal Symmetries of Strong Interactions

Abstract

Theorems relating the separate conservation of $C$ and $P$ in pion-nucleon interactions to $\mathrm{CP}$ invariance, the form of the interaction and the existence of a charge symmetry operation are generalized to other strong interactions. It is shown that the minimal conditions for the derivation of such results are the existence of a doublet structure for baryons and invariance under certain transpositions of the baryons that may be interpreted as generalized charge symmetries relating the different doublets and may be represented by reflection operations in an internal 4-dimensional space. If charge independence is also valid, highly symmetrical Yukawa couplings are obtained. The problem of the disagreement with experiment of such symmetric structures is analyzed in terms of additional quadrilinear interactions with lower symmetries which also possess the property that $P$ invariance follows from invariance under $\mathrm{CP}$. Various examples of such interactions are given. The possible application of the approximate symmetry principles considered to the weak interactions is briefly indicated.