In the usual description of the instanton of nonabelian gauge theory in $D=4$ spacetime, we always (or just usually?) choose the $D=4$ Euclidean spacetime see for example https://en.wikipedia.org/wiki/BPST_instanton.
In the interpretation of $D=4$ nonabelian gauge theory, we often freely Wick rotate the Euclidean spacetime to Minkowski spacetime.
My question --- do we really have a physical and mathematical rigorous description of instanton of nonabelian gauge theory in Minkowski spacetime? Or does the instanton only make sense in the Euclidean spacetime?
