  We construct an explicit example of dimensional reduction of the free
massless Dirac operator with an internal SU(3) symmetry, defined on a
twelve-dimensional manifold that is the total space of a principal SU(3)-bundle
over a four-dimensional (nonflat) pseudo-Riemannian manifold. Upon dimensional
reduction the free twelve-dimensional Dirac equation is transformed into a
rather nontrivial four-dimensional one: a pair of massive Lorentz spinor
SU(3)-octets interacting with an SU(3)-gauge field with a source term depending
on the curvature tensor of the gauge field. The SU(3) group is complicated
enough to illustrate features of the general case. It should not be confused
with the color SU}(3) of quantum chromodynamics where the fundamental spinors,
the quark fields, are SU(3) triplets rather than octets.
