It seems to me that in a path integral, since you are integrating over all field configurations, that going into Euclidean space is not valid because some field configurations will give poles in the integrand of your action, and when the integrand has poles you can't make the rotations required to make the integration limits take on real values. In other words, while you can always make the substitution [itex]t=-i\tau [/itex], in order to pretend [itex]\tau [/itex] is a real number and have the limits of integration over [itex]d\tau [/itex] be over real numbers, you need to be able to Wick rotate and that requires the field configurations in your action be well-behaved, but in the path integral the field configurations go over all values so aren't always well behaved.(adsbygoogle = window.adsbygoogle || []).push({});

So how is that you can justify going into Euclidean space in the path integral?

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# Continuing to Euclidean Space Justified in Path Integral?

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