A Model for the Broken SU(3) Symmetry Based on the Non-Linear Realization of the Group
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A composite model based on the non-linear realization of the group SU(3) on its subgroup U(2) is settled. The constituent particles are the nucleon, the pion and the kaon-pair which is a set of the preferred fields in the realization. First the minimal kaon-nucleon interaction is fixed through the classical Lagrangian density for the kaon-nucleon system, which is invariant under the group SU(3) in the sense of our realization. (§2) G-invariance is imposed on the Lagrangian density, but the neutral components of current, which belong to the homogeneous space SU(3)/U(2), have not definite CP parity in general owing to the non-linear character of our realization. Then the current-current type weak interaction with the selection rule |ΔI|=1/2 and |ΔY|=1 can involve the CP violating terms which induce the K_L^0-K_S^0 transition in the second order. (§3) In order to construct baryons as composite systems of the nucleon and the kaon, we must quantize these fields. The particle picture of the kaon is modified to avoid the difficulty in spanning the Fock space before the quantization, and the effective kaon-baryon interactions of the Yukawa type are extracted from the minimal interaction. (§4) The quantization of the modified kaon field as a Klein-Gordon particle introduces a breakdown of the symmetry even if any symmetry violating interaction is not considered. (§6) Further the operator of the composite Λ particle is not invariant under the group in our realization, for example. The pion problem is briefly discussed in §5.
- 理論物理学刊行会の論文
- 1972-04-25
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