  This paper is the SU(3) extension of the dynamically generated SU(2) linear
$\sigma$ model Lagrangian worked out previously using dimensional
regularization. After discussing the quark-level Goldberger-Treiman relations
for SU(3) and the related gap equations, we dynamically generate the meson
cubic and quartic couplings. This also constrains the meson-quark coupling
constant to $g=2\pi/\sqrt3$ and determines the SU(3) scalar meson masses in a
Nambu-Jona-Lasinio fashion. Finally we dynamically induce the U(3) pseudoscalar
and scalar mixing angles in a manner compatible with data.
