Some rather paradoxical features of chiral symmetry breaking are shown to be directly related to the fact that the vacuum is supposed to be degenerate in the limit of exact symmetry. The importance of picking the correct one of the many symmetry-limit vacua is stressed. A peculiar phenomena of spontaneous $\mathrm{CP}$ violation appearing alongside $\mathrm{SU}\left(3\right)\mathrm{}\otimes \mathrm{SU}\left(3\right)\mathrm{}$ breaking is observed. (In the model investigated here, the effect is much too large to be at all related to that seen in weak interactions.) For the $(3,\overline{3})\oplus (\overline{3},3)$ model of symmetry breaking, it is shown that the rate for $K_S^{}{}_{}{}^0\to 2\pi$ should be suppressed by a factor of ${\mathrm{}\left[SU\right(3\mathrm{})\mathrm{}\otimes \mathrm{SU}(3\left)\mathrm{} \mathrm{breaking}\right]}^4$. This may or may not be a difficulty. A number of other topics in chiral symmetry breaking are discussed briefly.

• Received 14 September 1970

DOI:https://doi.org/10.1103/PhysRevD.3.1879