  Differential geomtrical methods for deriving the Dirac equation in Curved
Spacetime are presented. Einstein's field equation is applied in a novel
manner; in the most current standard reference, Birrell and Davies, 1994 [1],
the suggestions for deriving the Dirac equation in Curved Spacetime make no
mention of employing Einstein's field equation. Thus, to date, the literature
on the derivation of the Dirac equation could not include an expression for the
presence of matter. This lack is consistent with earlier publications,
including Lichnerowicz's well-known 1964 journal article [3], which presented
the first such derivation, and Dimock's 1982 article [2]. The new differential
geometrical methods go beyond all previous suggestions, which only apply to
cases in the absence of matter. These differential geometrical methods have
resulted in derivations of the Dirac equation in Curved Spacetime that apply to
either the presence or absence of matter.
