# Proving that a Wick rotation is valid for a quantum field theory

While trying to find out if there is a rigorous justification for Wick rotating a QFT, I came across this other question (link below [1]) that mentions the Osterwalder-Schrader Theorem that gives a set of conditions under which Wick rotation is valid.

Now, my question is the following: Are the theories in which we normally use Wick rotation, such as QED or QCD, known to satisfy these conditions? In non-abelian gauge theories, we calculate instanton contributions to the path integral in Euclidean spacetime. I don't understand how this is valid in case the Euclidean fields don't satisfy the conditions in the Osterwalder-Schrader theorem.

Just about every particle physics computation is done via analytic continuation from Euclidean signature, either via Euclidean lattice simulations or via the $$+i\epsilon$$ prescription in perturbation theory. So in that sense, yes, Wick rotation is always valid for QFTs. (There are a handful of cases like Chern-Simons theory where the analytic continuation gets rather subtle.)