The course extends the T=0 calculations and diagrammatic technique to finite temperatures. The lectures include
- Imaginary time formalism, Matsubara frequencies
- Finite temperature Green's functions
- Diagrammatic rules, self-energy, Dyson equation
- Expressing physical quantities in terms of Green's functions
- Lehmann representation, linear response theory
- Discussion of the finite temperature interacting electron gas, screening, ring diagrams, interaction correction to the equation of state of an electron gas
- Superconductivity at finite temperatures within mean-field theory, normal and anomalous Green's functions
- Gap equation and its solution at T=0 and around the transition temperature, density of states, spectral function