Permutation Symmetry in Strong Interactions

It is assumed that there exist three basic fields ${\Phi }_1$, ${\Phi }_2$, and ${\Phi }_3$ and the Sakata triplet $p$, $n$, and $\Lambda$ which is related to the basic fields by a unitary transformation. Then, a meson-baryon interaction Hamiltonian that is invariant under $\mathrm{SU}\left(3\right)\mathrm{}$ is derived under the requirement that it should be invariant under permutations of ${\Phi }_1$, ${\Phi }_2$, and ${\Phi }_3$ and conserve charge and baryon number. A singlet fermion field is introduced in addition to the Sakata triplet in order to define the baryons in the octet case. Invariance under one permutation and conservation of isotopic spin, charge, and baryon number yield a Hamiltonian that is $\mathrm{SU}\left(3\right)\mathrm{}$-invariant. An explanation is given of how permutation symmetry $S_3$, the aformentioned unitary transformation, and two conservation laws lead to $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry.