20410022 - Quantum Theory of Matter

To offer an introduction to the methods of field theory applied to the study of many-body systems of Matter Physics. The course program includes in the first part the study of the perturbative methods and the theory of linear response applied to the electron gas with the use of Green functions and Feynman diagrams. In the second part the theoretical study of the quantum phenomena that characterize matter at low temperatures such as superfluidity and superconductivity is developed


teacher profile | teaching materials


- Fluctuation-dissipation theorem and linear response theory.
-Green functions at zero temperature. Lehmann decomposition. Analytical properties.
- Perturbative development and Feynman diagrams. Dyson equation.
- Green functions at finite temperature: Matsubara technique.
- Hartree-Fock theory and RPA approximation. Thomas-Fermi screen. Lindhard function.
-Fermi liquid theory.
- Phenomenology of superfluidity. Landau theory.
-Microscopic theory of superfluidity. Bogolubov theory.
- Phenomenology of superconductivity.
- Microscopic BCS theory of superconductivity.
-Gorkov's derivation of the Landau-Ginzburg equations.
-Theory of electronic transport in disordered systems.

Core Documentation

1- Carlo Di Castro, Roberto Raimondi, Statistical Mechanics and Applications in Condensed Matter, Cambridge University Press 2015.
2- Piers Coleman, Introduction to Many-Body Physics, Cambridge University Press 2015.

Type of delivery of the course

The lessons involve the detailed presentation of mathematical-formal developments and therefore the blackboard is used in a systematic way (or other digital instrument of equal effectiveness).

Type of evaluation

The final exam tends to understand whether the student has achieved a reasonable understanding of the topics. On the one hand, it is necessary to check that he has a general understanding of the various parts of the course and that he knows how to connect them together. For this reason, the oral exam consists partly of questions aimed at ascertaining these aspects without going into the details of the formalism and partly of questions in which you are asked to set the calculation of a specific physical effect. The evaluation is expressed in thirtieths.