The locally covariant Dirac field

Details The locally covariant Dirac field The locally covariant Dirac field

2009-11-06

arxiv.org/abs/0911.1304v2

Rev.Math.Phys.22:381-430,2010

Physics

Mathematical Physics

36 pages; v2 minor changes, typos corrected, updated references and acknowledgements

Scientific paper

10.1142/S0129055X10003990

We describe the free Dirac field in a four dimensional spacetime as a locally covariant quantum field theory in the sense of Brunetti, Fredenhagen and Verch, using a representation independent construction. The freedom in the geometric constructions involved can be encoded in terms of the cohomology of the category of spin spacetimes. If we restrict ourselves to the observable algebra the cohomological obstructions vanish and the theory is unique. We establish some basic properties of the theory and discuss the class of Hadamard states, filling some technical gaps in the literature. Finally we show that the relative Cauchy evolution yields commutators with the stress-energy-momentum tensor, as in the scalar field case.

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