Covariant harmonic oscillators and the quark model

The bound state model of Kim and Noz is reviewed and developed. The generalized overlap integral of covariant harmonic oscillators in different Lorentz frames is evaluated. The result is a covariant orthogonality relation, which allows a covariant probability interpretation for the wave functions. For excitations along the direction of motion, each half-wave is shown to be contracted by a factor of √(1 - β2). The model is then applied in calculating the axial-vector coupling constants in weak interactions. The static SU(6) prediction for -g/sub A/g/sub V/ (β decay), which is 5/3, is shown to be modified by the internal dynamics of the quarks. This modification brings the theoretical value much closer to the experimental value of 1.2. Results are included for other semileptonic baryon decays. Hyperfine splittings of nonstrange hadrons and charmonium are investigated with a relativistic gluon-exchange model. A formula is derived relating the Δ-N and rho-π mass differences where color and internal quark motion play an important role. For P-wave mass splittings, the L-vector.S-vector contributions are found to be too large; however, if the perturbing interaction is not pure vector in character, this L-vector.S-vector term can be suppressed. Finally, the strong decays of mesons and baryons are studied using covariant harmonic oscillators. The predictions of a quark-pair-creation model and a PCAC model are given, and the limitations of these approaches are discussed