Rationalizability of field extensions with a view towards Feynman integrals

TL;DR

This paper generalizes the concept of rationalizability from square roots to field extensions, providing a new method to determine the rationalizability of sets of polynomial square roots relevant to Feynman integrals.

Contribution

It introduces a generalized definition of rationalizability for field extensions and establishes an equivalence with the rationalizability of their compositum, offering a novel approach for Feynman integral analysis.

Findings

Rationalizability of quadratic field extensions is equivalent to that of their compositum.

Provides a new strategy to prove rationalizability of polynomial square roots.

Generalizes previous concepts to broader field extension contexts.

Abstract

In 2021, Marco Besier and the first author introduced the concept of rationalizability of square roots to simplify arguments of Feynman integrals. In this work, we generalize the definition of rationalizability to field extensions. We then show that the rationalizability of a set of quadratic field extensions is equivalent to the rationalizability of the compositum of the field extensions, providing a new strategy to prove rationalizability of sets of square roots of polynomials.