论文标题
因果扰动QED和白噪声。感应步骤
Causal perturbative QED and white noise. The inductive step
论文作者
论文摘要
我们介绍了Bogoliubov的因果扰动QFT，其中仅包括一种改进：在某个点上为特定动量的创建 - 通知操作员，\ emph {i.e。}，在数学上被解释为来自白噪声分析的HIDA操作员。我们将其余的理论完全保持不变。这允许在过渡到交互场的绝热极限中避免红外线和紫外线。在这里，我们提出了归纳步骤。我们特别关注对散射操作员的二阶贡献的分析，并使用积分内核操作员的计算进行明确的计算，\ emph {i.e}其矢量值值核的收缩，并将收缩的分配给高级零件。提供了QED的明确示例，以及避免紫外线差异的关键点的详细分析。
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.
