We derive an effective Hamiltonian of the relativistic quark model. In the limit of zero quark masses, we obtain linear Regge trajectories for mesons. Based on the diquark-antiquark symmetry, we show that the Regge trajectories of baryons and mesons are parallel at high angular moments. We discuss the breaking of the hadronic supersymmetry and obtain a mass relation of mesons and baryons.

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We propose a composite SU(2)×SU(2) Skyrme model which contains the original Skyrme model as a special case. We find that in one special case, the predicted pion decay constant is 185 MeV which is in excellent agreement with the experimental value of 186 MeV. Moreover, some other predicted static properties also agree well with the experiment, while a disagreement persists for the magnetic properties.

We propose a chiral Lagrangian in which the pions and the vector mesons are treated on equal footing. It gives the usual meson physics and a mass relation for the mesons. We introduce a soliton ansatz for the SU(4) Skyrme model which approximates the more realistic covariant theory. Upon quantization, a rich mass spectrum for the soliton is obtained.