论文标题
标量颗粒在1+3维度中的奇异光锥相互作用
Singular light cone interactions of scalar particles in 1+3 dimensions
论文作者
论文摘要
在这里，我们考虑了一个积分方程，描述了固定数量的标量粒子，该方程不是通过玻色子交换而不是直接沿光锥相互作用，就像在绑定状态方程（如伯特 - 盐）方程一样。该方程涉及一个多时间波函数$ψ（x_1，...，...，x_n）$，带有$ x_i =（t_i，\ mathbf {x} _i）\ in \ mathbb {r}^4 $作为重要概念。假设截止时间，我们证明它在最初的所有数据中都有一个唯一的解决方案。通过考虑特定弯曲的时空的积分方程，具有大爆炸奇点，在该方程中自然发生，而不会违反任何时空对称性。我们工作的主要特征是，我们将相互作用恰好发生在Minkowski距离为零的情况下，这反映了沿光锥的三角洲分布反映的相互作用。我们还将存在和唯一性结果扩展到任意数字$ n \ geq 2 $的粒子。总体而言，我们为1+3个时空维度中某种类型的相互作用相对论量子动力学提供了一个严格的示例。
Here we consider an integral equation describing a fixed number of scalar particles which interact not through boson exchange but directly along light cones, similarly as in bound state equations such as the Bethe-Salpeter equation. The equation involves a multi-time wave function $ψ(x_1,...,x_N)$ with $x_i=(t_i,\mathbf{x}_i) \in \mathbb{R}^4$ as a crucial concept. Assuming a cutoff in time, we prove that it has a unique solution for all data at the initial time. The cutoff is justified by considering the integral equation for a particular curved spacetime with a Big Bang singularity where an initial time occurs naturally without violating any spacetime symmetries. The main feature of our work is that we treat the highly singular case that interactions occur exactly at zero Minkowski distance, reflected by a delta distribution along the light cone. We also extend the existence and uniqueness result to an arbitrary number $N \geq 2$ of particles. Overall, we provide a rigorous example for a certain type of interacting relativistic quantum dynamics in 1+3 spacetime dimensions.
