Abstract

We present Bogoliubov’s causal perturbative QFT with only one refinement: the creation–annihilation operators at a point, i.e., for a specific momentum, are mathematically interpreted as the Hida operators from the white noise analysis. We leave the rest of the theory completely unchanged. This allows avoiding infrared (and ultraviolet) divergences in the transition to the adiabatic limit for interacting fields and eliminating the free parameters of the theory associated with the choice of normalization in computation of the retarded and advanced parts of causal distributions (corresponding to the freedom in choosing the renormalization scheme). This enhances the predictive power of the theory, and in particular allows deriving nontrivial mass relations. The approach is general and can be applied to investigate any perturbative QFT.

中文翻译：

---

因果微扰 QED 和白噪声

摘要

我们提出了 Bogoliubov 的因果微扰 QFT，仅进行了一项改进：在一点（即针对特定动量）的创建-湮灭算子在数学上被解释为来自白噪声分析的 Hida 算子。我们保留理论的其余部分完全不变。这可以避免在相互作用场向绝热极限过渡时出现红外（和紫外）发散，并消除与因果分布的延迟和高级部分计算中归一化选择相关的理论自由参数（对应于选择重整化方案）。这增强了理论的预测能力，特别是允许推导非平凡的质量关系。该方法是通用的，可用于研究任何微扰 QFT。