论文标题
QED是一种多体的世界理论：ii。全阶S-Matrix形式主义
QED as a many-body theory of worldlines: II. All-order S-matrix formalism
论文作者
论文摘要
在ARXIV：2206.04188中，我们开发了一种首先量化的世界形式主义，用于QED中振幅的全阶计算。特别是，我们在此框架中证明了Faddeev-Kulish（FK）S-Matrix的红外安全性，以进行带电费米子散射的虚拟交换。在这项工作中，我们扩展了戴森和FK S-Matrix的全球形式主义，以进一步考虑任意数量的光子的排放和吸收。我们展示了Low的定理在此框架中如何遵循，并得出了Weinberg的IR差异定理。特别是，我们将FK S-Matrix的IR安全性的全阶证明扩展到虚拟交换和实际光子排放。我们认为，全球方法导致了对FK S-Matrix的IR安全性的现代威尔逊主义解释，并为在实时问题中处理IR差异提供了一种新颖的模板。使用Grassmannian的整合方法，我们为n-th Rank真空极化张量提供了简单而有力的结果。这些方法的应用将在后续工作中讨论。
In arXiv:2206.04188, we developed a first-quantized worldline formalism for all-order computations of amplitudes in QED. In particular, we demonstrated in this framework an all-order proof of the infrared safety of the Faddeev-Kulish (FK) S-matrix for virtual exchanges in the scattering of charged fermions. In this work, we extend the worldline formalism for both the Dyson and FK S-matrix to consider further the emission and absorption of arbitrary numbers of photons. We show how Low's theorem follows in this framework and derive Weinberg's theorem for the exponentiation of IR divergences. In particular, we extend our all-order proof of the IR safety of the FK S-matrix to both virtual exchanges and real photon emissions. We argue that the worldline approach leads to a modern Wilsonian interpretation of the IR safety of the FK S-matrix and provides a novel template for the treatment of IR divergences in real-time problems. Using Grassmannian integration methods, we derive a simple and powerful result for N-th rank vacuum polarization tensors. Applications of these methods will be discussed in follow-up work.
