Adiabatic Hadamard States for Dirac Quantum Fields on Curved Space

S. Hollands

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arXiv · gr-qc/9901069

Adiabatic Hadamard States for Dirac Quantum Fields on Curved Space

S. Hollands

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Abstract

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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S. Hollands. 1999-01-25. Adiabatic Hadamard States for Dirac Quantum Fields on Curved Space. https://arxiv.org/abs/gr-qc/9901069

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