I can't find any good references on Euclideanizing path integrals (from Minkowski to Euclidean metric). I understand how this is done in perturbative 1-loop calculations, where the pole structure of the Feynman propagators are used to perform the so-called Wick Rotation. This seems to be a perfectly valid procedure in light of complex analysis (in particular, Cauchy's theorem). However, in path integrals, there are no poles per-se. How is the passage into imaginary time justified? AND does such Euclideanization always yield a Hamiltonian in the exponent?