9- Retarded and advanced Green's functions - Course on Quantum Many-Body Physics

Description: Welcome to the course on Quantum Theory of Many-Body systems in Condensed Matter at the Institute of Physics - University of Sao Paulo (IF-USP). In this class, we will cover: Single-particle Green’s functions. Retarded and advanced Green’s functions. Many-particle Green’s functions Lehmann representation. Nice paper by Odashima et al on the basics of Green's functions: https://arxiv.org/abs/1604.02499 0:00 Introduction 1:03 Single-particle Green's functions (time-independent) 11:11 Lippmann-Schwinger's Equation 37:00 Single-particle Green's functions (time-dependent) 40:24 Retarded Green's functions 48:25 Many-particle Green's functions 50:50 Advanced, Greater and Lesser Green's functions 57:11 Lehmann representation 1:14:39 Spectral Function ERRATUM: At 52:40 , it should be + for bosons and - for fermions.