Physics 582 (QFT I) Fall 2010 Lecture on Monday October 12, 2020. Today we covered the computation of the path integral for the free massive scalar field in Euclidean spacetime and used the results to compute the propagator in Euclidean and Minkowski spacetimes as well as extracting their short and long distance behaviors. We also discuss the relation between mass gaps and exponential decays of correlation functions in imaginary time.