Is there a good reference on the procedure of Euclideanizing the action? In particular, giving a detailed account of Wick rotating in this context. I can't seem to figure out if they are supposed to give precisely the same answer (even numerically), but just that one converges better, or if they are two different quantities (just one related to the other). Also, is there a standard way of Euclideanizing the fermionic action and the spin-1 Yang Mills action? There seem to be subtleties which seems very poorly motivated. For example, multiplying [itex]\sigma^0[/itex] and [itex]A^0[/itex] by the imaginary unit, [itex]i[/itex].