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We obtain a complete set of free-field solutions of the Dirac equation in a(longitudinal) boost-invariant geometry with azimuthal symmetry and use thesesolutions 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 $\tau = (t^2-z^2)^{1/2}$ isrelevant for understanding particle production of quarks and antiquarksfollowing an ultrarelativistic collision of heavy ions, as it incorporates the(approximate) longitudinal "boost invariance" of the distribution of outgoingparticles. We compare two approaches to solving the Dirac equation incurvilinear coordinates, one directly using Vierbeins, and one using a"diagonal" Vierbein representation

Forward cone quantization of the Dirac field in “longitudinal boost-invariant” coordinates with cylindrical symmetry