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

Claudio Dappiaggi, Thomas-Paul Hack, Nicola Pinamonti
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.
@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