English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this article, we study functional analytic properties of the meromorphicfamilies of distributions $(\prod_{i=1}^p(f_j+i0)^{\lambda_j})_{(\lambda_1,\dots,\lambda_p) \in \mathbb{C}^p}$ usingHironaka's resolution of singularities, then using recent works on thedecomposition of meromorphic germs with linear poles, we renormalize productsof 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 propertiesof $(\prod_{i=1}^p(f_j+i0)^{\lambda_j})_{(\lambda_1,\dots,\lambda_p)\in\mathbb{C}^p}$ and$\prod_{i=1}^p (f_j+i0)^{k_j}, k_j \in \mathbb{Z}$. In the second part, weargue that the above families of distributions with \emph{regular holonomicsingularities} provide a universal model describing singularities of Feynmanamplitudes and give a new proof of renormalizability of quantum field theory onconvex analytic Lorentzian spacetimes as applications of ideas from the firstpart.

Complex powers of analytic functions and meromorphic renormalization in QFT