The question arises when I'm reading over the section "3.3.1 Minkowski Space" in page 16-17 in the following link: https://www-thphys.physics.ox.ac.uk/people/JohnCardy/qft/qftcomplete.pdf
It is discussing the technique of using Wick Rotation to calculate the generating function in Minkowski space.
It mentioned that simply inserting τ=it into the results of the generating function in Euclidean space (i.e. imaginary time) provides the generating function in Minkowski space.
However, on top of page 17, it mentioned that I also have to let p0 --> ip0 as well. Why do I have to do this as well? How is that related to defining τ=it and making a Wick Rotation?