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

April 03, 2009

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.

open access link
Rev.Math.Phys.21:1241-1312,2009

@article{Dappiaggi:2009xj,
author = "Dappiaggi, Claudio and Hack, Thomas-Paul and Pinamonti,
Nicola",
title = "{The Extended algebra of observables for Dirac fields and
the trace anomaly of their stress-energy tensor}",
journal = "Rev. Math. Phys.",
volume = "21",
year = "2009",
pages = "1241-1312",
doi = "10.1142/S0129055X09003864",
eprint = "0904.0612",
archivePrefix = "arXiv",
primaryClass = "math-ph",
reportNumber = "DESY-09-049, ZMP-HH-09-9",
SLACcitation = "%%CITATION = ARXIV:0904.0612;%%"
}

Keywords:

Dirac fields, QFT on curved spacetimes, trace anomaly