Symmetry of the Strong Interaction in the Four-Dimensional Isotopic-Spin Space and in the Three-Dimensional κ-Space

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Without using strangeness a variant theory of higher symmetry is proposed for the strong interactions of baryons. We classify baryons into two groups : (pnΞ^0Ξ^-) called the p-group and (Σ^+Σ^0Σ^-Λ) called the q-group in terms of a new quantum number κ_3=1/2 for the p-group and κ_3=-1/2 for the q-group. p and q make a spinor in the three-dimensional κ-space. Each group is, in turn, considered to represent a vector in the four-dimensional isotopic spin space, called N-space, which can be reduced to define two sets of spin matrices τ and ζ, the sum of the third components of which are related to the electric charge of baryons : Q_e=τ_3+ζ_3. In order to give an interaction Hamiltonian symmetric in κ-space and also in N-space, which are orthogonal to each other, we introduce sixteen kinds of mesons with spin 0 which mediate the strong interactions of the Yukawa type among baryons. Under the requirement of rotational invariance for the interaction Hamiltonian in the N-κ space, the character of mesons is naturally defined. It is shown that pions correspond to the component of κ_3=0, κ=0 ; strangeness-two mesons to κ_3=0, κ=1 ; and kaons to κ_3=±1, κ=1. We introduce two kinds of kaons, one called K-kaons exclusively coupling nucleons with the Σ- and Λ-particles and the other called L-kaons coupling the Ξ-particle with the Σ- and Λ-particles. It is shown that our scheme covers the current theory of higher symmetry and the strangeness rule, with the additional selection rule Δκ_3=0 which enables us to forbid the processes : Ξ^-+p→Λ+Λ, D^-+p+p→Σ^++Λ, etc. A number of experiments in hyperon-meson physics are, therefore, proposed which permit a selection between our scheme and the current theory.
理論物理学刊行会の論文
1961-08-25

Symmetry of the Strong Interaction in the Four-Dimensional Isotopic-Spin Space and in the Three-Dimensional κ-Space

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