Quantum field theory in static external potentials and Hadamard states

Details Quantum field theory in static external potentials and Hadamard states Quantum field theory in static external potentials and Hadamard states

2011-08-15

arxiv.org/abs/1108.2982v2

Physics

Mathematical Physics

30 pages; v2 revised, accepted for publication in Annales Henri Poincare

Scientific paper

We prove that the ground state for the Dirac equation on Minkowski space in static, smooth external potentials satisfies the Hadamard condition. We show that it follows from a condition on the support of the Fourier transform of the corresponding positive frequency solution. Using a Krein space formalism, we establish an analogous result in the Klein-Gordon case for a wide class of smooth potentials. Finally, we investigate overcritical potentials, i.e. which admit no ground states. It turns out, that numerous Hadamard states can be constructed by mimicking the construction of ground states, but this leads to a naturally distinguished one only under more restrictive assumptions on the potentials.

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