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

TL;DR

This paper develops a covariant quantum field theory framework for Dirac spinors on curved spacetimes, introduces Wick polynomials, and computes the trace anomaly of the stress-energy tensor.

Contribution

It provides a rigorous construction of Dirac fields as a locally covariant quantum theory and explicitly calculates the trace anomaly for their stress-energy tensor.

Findings

Constructed a covariant quantum field theory for Dirac spinors.

Developed Wick polynomials for spinor fields.

Explicitly computed the trace anomaly.

Abstract

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.