Quantum field theory in static external potentials and Hadamard states

Abstract

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.

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

References in corpus (2)

• Divergences in quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential
• Scattering theory for Klein-Gordon equations with non-positive energy

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• A new class of Fermionic Projectors: Møller operators and mass oscillation properties
• Vacuum polarization near boundaries
• States of low energy in the Schwinger effect