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Solutions of the Bethe-Salpeter equation with dual interaction kernel for baryons and $$\text{SU}(6)\otimes\text{O}(3)_{L}$$ symmetry. (English) Zbl 1079.81527
Summary: The Bethe-Salpeter equations for baryons are solved in the relativistic quark model. The dual interaction kernel is used. Spatial parts of the Bethe-Salpeter amplitudes are given by the factorized residues at poles of the interaction kernel. By introducing eigenvalues of integration kernels all possible spinor forms are shown to five solutions. Physicality conditions for eigenvalues and their energy-derivatives at resonance points play a very important role to discriminate these solutions: Spinor wave functions which appear in SU(6) theory satisfy the physicality conditions and others do not. Our theory explains, therefore, $$SU(6)\otimes O(3)_L$$ symmetry as a dynamical consequence of the relativistic composite theory.

MSC:
 81Q40 Bethe-Salpeter and other integral equations arising in quantum theory
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