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arXiv · 2507.16085

Singularities of Dirac-Coulomb propagators

Dean Baskin·Michał Wrochna·Jared Wunsch
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Abstract

In this paper we study singularities of propagators and $N$-point functions for Dirac fields in a Coulomb potential, possibly with a $t$-dependent smooth part for $|t|<T<\infty$. We show that the in and out Dirac-Coulomb vacua are Hadamard states for $r\neq 0$. Furthermore, we prove that the relative charge density of any two Hadamard states is well-defined as a locally integrable function including near $r=0$. The results are based on a diffractive propagation of singularities theorem for the Dirac-Coulomb system previously obtained by the first and third authors, generalized here to the case of $t$-dependent potentials.

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Dean Baskin, Michał Wrochna, Jared Wunsch. 2025-07-21. Singularities of Dirac-Coulomb propagators. https://arxiv.org/abs/2507.16085

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