  We discuss from scratch the classical structure of Dirac spinors on an
arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a
locally covariant quantum field theory, and the associated notion of a Hadamard
state. Eventually, we develop the notion of Wick polynomials for spinor fields,
and we employ the latter to construct a covariantly conserved stress-energy
tensor suited for back-reaction computations. We shall explicitly calculate its
trace anomaly in particular.
