因果微扰 QED 与白噪声：归纳步骤
Causal perturbative QED and white noise. The inductive step
AI总结：
本文提出在 Bogoliubov 因果微扰 QFT 中将产生-湮灭算子解释为白噪声分析中的 Hida 算子，通过归纳步骤分析散射算子二阶贡献，避免了相互作用场的红外和紫外发散。
摘要：
我们提出了 Bogoliubov 的因果微扰 QFT，其中仅包含一项改进：将某一点（即特定动量下）的产生-湮灭算子在数学上解释为白噪声分析中的 Hida 算子。理论的其余部分保持完全不变。这使得在相互作用场向绝热极限过渡时，能够避免红外和紫外发散。本文呈现归纳步骤。我们着重分析散射算子的二阶贡献，并利用积分核算子微积分（即其向量值核的收缩，以及将收缩分为超前和滞后部分）进行显式计算。文中提供了 QED 的具体示例，并对避免紫外发散的关键点进行了详细分析。
英文摘要：
We present the Bogoliubov's causal perturbative QFT, which includes only one refinement: the creation-annihilation operators at a point, \emph{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. Here we present the inductive step. We are especially concentrated with the analysis of the second order contribution to the scattering operator, and give explicit computations using the calculus of integral kernel operators, \emph{i.e} contractions of their vector-valued kernels, and splittings of the contractions into advanced and retarded parts. Explicit example of QED is provided, together with the detailed analysis of the key point in avoiding UV divergence.
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