Geometric Singularities of Feynman Integrals

TL;DR

This paper introduces a novel method to analyze the singularities of Feynman integrals by associating a constructible function with the PDE system, enabling direct reading of singularities and applicable across various representations.

Contribution

It presents a new, explicit approach to determine the singularities of Feynman integrals using constructible functions, independent of the PDE system's explicit form.

Findings

Allows direct identification of singularities from the constructible function.

Applicable to multiple representations of Feynman integrals.

Provides a flexible framework for analyzing Feynman integral singularities.

Abstract

We provide a new method to calculate the full microlocal description of singularities of Feynman integrals. This is done by associating a unique constructible function to the system of partial differential equations (PDEs) annihilating the integral and from this function the singularities can directly be read-off. This function can be constructed explicitly even if the system of PDEs is unknown and describes both the location of the singularities and the number of master integrals on them. Our framework is flexible enough to preform the calculation in any of the Lee-Pomeransky, Feynman, or momentum representations.