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We discuss from scratch the classical structure of Dirac spinors on anarbitrary globally hyperbolic, Lorentzian spacetime, their formulation as alocally covariant quantum field theory, and the associated notion of a Hadamardstate. Eventually, we develop the notion of Wick polynomials for spinor fields,and we employ the latter to construct a covariantly conserved stress-energytensor suited for back-reaction computations. We shall explicitly calculate itstrace anomaly in particular.

The extended algebra of observables for Dirac fields and the trace anomaly of their stress-energy tensor