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  • $\begingroup$ Just want to add that, this complex trajectory of functional integral is just a generalization of contour integral of one single variable. Say you are doing $\int dx \, f(x)$ along the real axis. As long as you don't hit a singularity of $f$, you can have the contour run wild in the complex plane and still get the right answer. Same thing. $\endgroup$ Commented Nov 26, 2024 at 15:52
  • $\begingroup$ $\uparrow$ Right. $\endgroup$ Commented Nov 26, 2024 at 15:54