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I'm writing a (semi)popular science book about fundamental physics (in Dutch). I want to include a section about Wick rotations in the path integral (in the context of Hawkings no-boundary proposal, but let's keep quantum gravity out for the moment and stick to ordinary QFT). I've read many blogs and papers about a justification (like Lubos Motl's blog and a dozen of QFT books like "Gifted amateur", Peskin&Schroeder, Srednicki, Zee, etc) and I just can't see how I would explain it conceptually to a laymen (or graduate student, for all that matters). besides a "shut up and calculate" kind of answer.

I'd like to compare Wick rotation to the renormalization hypothesis, which says that divergencies in Feynmandiagrams are encountered due to the use of naked parameters instead of physical ones. Is there any similar "hypothesis" about why we can use Wick rotations? Up to now I have the impression that the reasoning is like "well, the path integral is ill-defined anyway so let's try an analytical continuation, because the correspondence between QFT and thermodynamics in equilibrium looks so nice. This analytic continuation is unique, so if it gives a sensible answer we can compare with experiments and only wonder about a possible physical deaper meaning of this trick."

I guess something similar goes for zeta-function regularization in e.g. the Casimir effect or string theory, in which one analytically continues the zeta function to obtain a finite answer to the sum of all integers.

I also see that for the propagator a Wick rotation is equivalent to the usual ##i\epsilon##-prescription, which regulates the Green's function by imposing an infinitesimal damping and as a bonus includes boundary conditions. But this does not automatically implies full equivalence with the Wick rotation of the path integral, right?

I hope my question is clear. If someone could make me more comfortable with this Wick-rotation business and give me a conceptual explanation of why we are allowed to do it/a decent philosophy behind it, I'd be happy. And if someone can supplement it with simple algebraic examples, I'd be even more happy.

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# A Feeling uncomfortable about Wick-rotations

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