Euclidean Path Integral: Introduction and Applications

This lecture introduces the concept of the Euclidean path integral, explaining the Euclidean action, time, correlation functions, and Wick rotation. The instructor discusses the connection of Euclidean methods with quantum field theory and statistical mechanics, emphasizing the usefulness of perturbation theory using Feynman diagrams. The lecture covers the idea of coupling a system to an external source to measure its response, illustrating this concept in the context of quantum mechanics. The instructor explains the path integral representation for correlation functions and the transition amplitude in quantum mechanics, highlighting the significance of Euclidean path integrals in theoretical physics. The lecture concludes with a detailed explanation of the Euclidean path integral representation for the partition function of quantum systems at finite temperature, showcasing its importance in statistical mechanics.