Singularities of Dirac-Coulomb propagators
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918101247852544 |
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| author | Baskin, Dean Wrochna, Michał Wunsch, Jared |
| author_facet | Baskin, Dean Wrochna, Michał Wunsch, Jared |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16085 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singularities of Dirac-Coulomb propagators Baskin, Dean Wrochna, Michał Wunsch, Jared Mathematical Physics Analysis of PDEs 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. |
| title | Singularities of Dirac-Coulomb propagators |
| topic | Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2507.16085 |