(Received November 1, 1973)
It is shown that the Bethe-Salpeter equation with the interaction kernel determined by the dual realistic quark model do not have the solutions of scalar and axial vector types with respect to spinor indices. The reason why only the pseudoscalar and vector type solutions exist is clarified. It is concluded, therefore, that our theory allows only the SU(6)-type solutions for one-meson states at rest. Our interaction kernel prohibits naturally quarks from appearing as free particle in the incoming and outgoing states. Normalization of the solutions is discussed. Our theory becomes much simpler by taking the mass of the quark to be infinity at the last stage of calculation, the remaining parameters being the coupling constant, slope and zero intercept of the leading orbital Regge trajectory. It is suggested that this limit may have some connections with the dual string model where end points of the string are interpreted to be the valence quark and antiquark which carry the degrees of freedom of unitary spin, spin and spatial coordinates.
URL : http://ptp.ipap.jp/link?PTP/51/1551/
DOI : 10.1143/PTP.51.1551