  Consider a formally self-adjoint first order linear differential operator
acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold
without boundary. We examine the geometric content of such an operator and show
that it implicitly contains a Lorentzian metric, Pauli matrices, connection
coefficients for spinor fields and an electromagnetic covector potential. This
observation allows us to give a simple representation of the massive Dirac
equation as a system of four scalar equations involving an arbitrary two-by-two
matrix operator as above and its adjugate. The point of the paper is that in
order to write down the Dirac equation in the physically meaningful
4-dimensional hyperbolic setting one does not need any geometric constructs.
All the geometry required is contained in a single analytic object - an
abstract formally self-adjoint first order linear differential operator acting
on pairs of complex-valued scalar fields.
