Why do we Wick rotate before regularizing Feynman diagrams?

Question

In Folland's Quantum Field Theory he mentions that we can apply Feynman's formula (Feynman parameterization) to either the Wick rotated integrals or the non-Wick rotated integrals corresponding to Feynman diagrams. However, later in the section he outlines a regularization procedure, in which he says we must first Wick rotating the integrals. Why is this Wick rotation necessary? Is it to make use of certain properties of Euclidean space that are not shared by Minkowski space? If so, which ones?

Answer 1

Well, as long as the singularities of the propagators in Minkowski signature are regularized with a Feynman $i\epsilon$ prescription, Wick rotation is in principle not necessary. However in practice, the loop momentum integrals of the Feynman diagram are simpler to evaluate in Euclidean signature, e.g. because $SO(d)$ symmetry is simpler to handle than $SO(d-1,1)$ symmetry.

See also this related Phys.SE post.