Appears in collection : 2026 IHES Summer School – Cosmological Correlators

This lecture develops the path-integral description of open quantum systems using the closed time contour. Topics include: - The Schwinger–Keldysh (in-in) formalism, - Doubling of fields and the structure of the closed time path, - In-in Feynman rules and perturbation theory for open systems, retarded, advanced and Keldysh propagators, - Noise, dissipation, and influence functionals, - Constraints from ultraviolet unitarity, locality, and symmetries. The equivalence between operator and path-integral approaches is emphasized, together with the structural constraints imposed by unitarity and symmetries at high energies.