  We apply the chiral color dielectric model to low- and medium-energy
scattering within the coupled $\pi$N and $\pi\Delta$ system. Dynamic baryon
states in which quarks are confined by the scalar color-dielectric field are
constructed in Fock space. Spurious motion of the center of mass is eliminated
by constructing momentum eigenstates via a Peierls-Yoccoz projection. The
relativistic Lippmann-Schwinger equation is solved for the complex energies of
the T matrix poles, and the pole positions of the nucleon and delta are used to
fix the few parameters of the model. The $S$- and $P$-wave phase shifts, the
bare N and $\Delta$ masses, the renormalized $\pi$NN and $\pi$N$\Delta$
coupling constants, and the $\pi$NN and $\pi$N$\Delta$ vertex functions are
predicted. nucleon and delta are used to fix the few parameters of the model.
The $S$- and $P$-wave phase shifts, the bare N and $\Delta$ masses, the
renormalized $\pi$NN and $\pi$N$\Delta$ coupling constants, and the $\pi$NN and
$\pi$N$\Delta$ vertex functions are predicted.

Nuclear Theory