标题： 解析函数的复幂和量子场论中的亚纯重整化 显示英文标题

标题： Complex powers of analytic functions and meromorphic renormalization in QFT

摘要： 在本文中，我们研究了全纯分布族$(\prod_{i=1}^p (f_j+i0)^{\lambda_j})_{(\lambda_1,\dots,\lambda_p) \in \mathbb{C}^p}$的函数分析性质，使用了Hironaka的奇点解消，然后利用最近关于具有线性极点的全纯芽分解的研究，我们在分布空间中对解析函数幂的乘积$\prod_{i=1}^p(f_j+i0)^{k_j}, k_j \in \mathbb{Z}$进行了重整化。我们还研究了$(\prod_{i=1}^p (f_j+i0)^{\lambda_j})_{(\lambda_1,\dots,\lambda_p)\in\mathbb{C}^p}$和$\prod_{i=1}^p (f_j+i0)^{k_j}, k_j \in \mathbb{Z}$的微局部性质。在第二部分中，我们认为上述带有\emph{正则的奇异奇点}的分布族提供了一个描述费曼振幅奇点的通用模型，并作为第一部分思想的应用，给出了量子场论在凸解析洛伦兹时空上的可重整化的新的证明。 显示英文摘要

摘要： In this article, we study functional analytic properties of the meromorphic families of distributions $(\prod_{i=1}^p (f_j+i0)^{\lambda_j})_{(\lambda_1,\dots,\lambda_p) \in \mathbb{C}^p}$ using Hironaka's resolution of singularities, then using recent works on the decomposition of meromorphic germs with linear poles, we renormalize products of powers of analytic functions $\prod_{i=1}^p(f_j+i0)^{k_j}, k_j \in \mathbb{Z}$ in the space of distributions. We also study microlocal properties of $(\prod_{i=1}^p (f_j+i0)^{\lambda_j})_{(\lambda_1,\dots,\lambda_p)\in\mathbb{C}^p}$ and $\prod_{i=1}^p (f_j+i0)^{k_j}, k_j \in \mathbb{Z}$. In the second part, we argue that the above families of distributions with \emph{regular holonomic singularities} provide a universal model describing singularities of Feynman amplitudes and give a new proof of renormalizability of quantum field theory on convex analytic Lorentzian spacetimes as applications of ideas from the first part.