Symmetry Laws and Strong Interactions

An attempt is made to explore the possible connection between symmetry laws in internal space (e.g., isospin space) and symmetry laws in Lorentz space with special attention to the question: Why are the strong interactions parity-conserving? For direct (non-derivative-type) pion-nucleon interactions, $\mathrm{CP}$ invariance and charge independence are sufficient to guarantee the separate conservation of $P$ and $C$, as previously pointed out. For derivative-type pion-nucleon interactions, charge independence and $G$ invariance (rotational and inversion invariance in three-dimensional isospin space) require that parity (and $\mathrm{CP}$) be conserved; in addition we can also show that the charge-triplet pion must be pseudoscalar, provided that the virtual Yukawa process ${\pi }^0\rightleftarrows p+\overline{p}$ is allowed or, equivalently, the ${\pi }^0$ can be regarded as a bound state of a proton and an antiproton as far as symmetry laws are concerned. For the $K$ couplings, analogous conditions cannot be obtained from the usual assumption of charge independence alone. However, if the $K$ couplings (rather than the $\pi$ couplings) exhibit a higher internal symmetry in the sense that the $K$ couplings are universal, the high $K$ symmetry plus charge independence in the usual sense imply parity conservation both in the case of $\mathrm{CP}$-invariant nonderivative-type $K$ interactions and in the case of $G$-invariant derivative-type $K$ interactions. The high $K$ symmetry also implies that the relative $N\Xi$ parity as well as the relative $\Lambda \Sigma$ parity is even. It is conjectured that, if the $K$ couplings must be of a derivative type, only $ps-pv$ coupling is allowed, which means that the $K$ particle is pseudoscalar. The global symmetry model which cannot be reconciled with our assumption of the high $K$ symmetry is re-examined. The high $K$ symmetry is destroyed in a specific and definite manner by the $\pi$ couplings, and relations among the various coupling constants are inferred from the baryon mass spectrum. Some empirical implications of our model are discussed. Whereas $G$ invariance requires the symmetric appearance of the two chiral spinors $\frac{1}{2}(1+{\gamma }_5)\psi$ and $\frac{1}{2}(1-{\gamma }_5)\psi$ for strangeness-conserving processes, for strangeness-nonconserving processes $G$ conjugation carries charge-conserving interactions into inadmissible interactions that do not conserve electric charge. Hence, if we take the point of view that parity-conserving interactions are generated by $G$ conjugation, we have some understanding of the puzzling fact that strangeness conservation and parity conservation have the same domain of validity. Further theoretical speculations are made.