Gluon propagator in the soliton bag model and its applications

The linearized quantum chromodynamics propagator for gluons is identical to that of electrodynamics. In models of QCD, the vacuum is medium with dielectric properties for gluon propagator. This is the case for the non-topological soliton model where the dielectric function kappa is introduced as a function of sigma, the scalar field of the model. Kappa = 0 at the vacuum value yields color confinement. The differential equations for the gluon propagator are derived in medium, i.e., for an arbitrary dielectric function in terms of vector spherical harmonics. The Coulomb gauge is used: the scalar Green function is instantaneous and the frequency-dependent tensor Green function is transverse. The mean field equations for baryons and mesons are solved including one gluon exchange terms. The quark, sigma, and gluon equations are treated self-consistently. Various baryon and meson properties are calculated and compared with numerical results based on perturbative calculations and on the free (kappa = 1) propagator. In the case of spectra, the effect of use of a confined vs. free propagator is primarily a renormalization of the effective gluon coupling constant. However, dynamical calculations, those in which the cavity changes size and shape, will require the use of a confined propagator