标题： 狄拉克-库仑传播子的奇点 显示英文标题

标题： Singularities of Dirac-Coulomb propagators

摘要： 在本文中，我们研究了在库仑势中狄拉克场的传播子和$N$点函数的奇点，可能包含一个与$t$有关的平滑部分对于$|t|<T<\infty$。 我们证明了入射和出射的狄拉克-库仑真空是 Hadamard 状态对于$r\neq 0$。 此外，我们证明了任何两个 Hadamard 状态的相对电荷密度作为局部可积函数是良好定义的，包括在$r=0$附近。 这些结果基于由第一作者和第三作者之前获得的狄拉克-库仑系统的奇异点衍射传播定理，这里将其推广到$t$依赖势的情况。 显示英文摘要

摘要： 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.