Euclidean Path Integral: Correlation Functions

This lecture delves into the concept of Euclidean path integrals, focusing on correlation functions. The instructor explains the Euclidean time integral, boundary conditions, and the operator meaning of the canonical quantization. By discussing the limit as beta goes to infinity, the lecture demonstrates how vacuum expectation values of time-ordered products can be obtained as path integrals. The weak rotation from imaginary to real time is explored, showcasing how different orderings in real time can be derived from Euclidean correlators. The analytic domain of correlation functions is discussed, emphasizing the importance of Euclidean correlation functions in obtaining real-time correlators with various orderings.