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Apr 16, 2020 at 22:24 comment added John Dougherty I would interpret "perform the saddle point approximation" to mean "replace the total integral on the left with the integral over the critical points on the right". When you perform the saddle point approximation you throw out everything except for the critical points, which have finite action. So once you perform the saddle point approximation there are only finite action contributions to the new integral.
Apr 16, 2020 at 22:15 comment added adithya So is it essentially saying that once you perform the saddle point approximation, then in the remaining gaussian path integral, there are no finite action contributions as @Chiral_Anomaly mentioned in their answer?
Apr 16, 2020 at 22:07 history answered John Dougherty CC BY-SA 4.0