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

Understand

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.