  We obtain a complete set of free-field solutions of the Dirac equation in a
(longitudinal) boost-invariant geometry with azimuthal symmetry and use these
solutions to perform the canonical quantization of a free Dirac field of mass
$M$. This coordinate system which uses the 1+1 dimensional fluid rapidity $\eta
= 1/2 \ln [(t-z)/(t+z)]$ and the fluid proper time $\tau = (t^2-z^2)^{1/2}$ is
relevant for understanding particle production of quarks and antiquarks
following an ultrarelativistic collision of heavy ions, as it incorporates the
(approximate) longitudinal "boost invariance" of the distribution of outgoing
particles. We compare two approaches to solving the Dirac equation in
curvilinear coordinates, one directly using Vierbeins, and one using a
"diagonal" Vierbein representation.
