Rationalizability of field extensions with a view towards Feynman integrals

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.