Adiabatic Hadamard States for Dirac Quantum Fields on Curved Space

Details Adiabatic Hadamard States for Dirac Quantum Fields on Curved Space Adiabatic Hadamard States for Dirac Quantum Fields on Curved Space

1999-01-25

arxiv.org/abs/gr-qc/9901069v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, Latex

Scientific paper

In this paper we propose a definition of quasifree Hadamard states for spinor fields on a curved space-time by specifying the Polarisation Set of the two-point function. We prove that the thermal equilibrium state on an ultrastatic space-time is Hadamard. We then construct an adiabatic vacuum state on a general globally hyperbolic Lorentz manifold using a factorisation of the spinorial Klein-Gordon operator. This state is pure. In what constitutes the main part of the paper, we show that it is also Hadamard. As a side result, we obtain the propagation of singularities of the spinorial Klein-Gordon operator. Some notation and results are collected in the Appendix.

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