Single-Course English 5 ECTS

Many body methods in condensed matter physics

Overall Course Objectives

The technology to fabricate optical electronic devices based on nanostructures and low-dimensional materials is progressing rapidly. These systems possess, apart from forming the basis for future electronic components, many fascinating physical properties and research in this field is a central topic in modern condensed matter physics. The theoretical description requires advanced techniques based on many-body theory (e.g., Green functions and diagrammatic perturbation theory). The general goal of this course is to give the student some general acquaintance with these analytical techniques and their applications to relevant systems, as well as an overview of the basic physics. This course also gives sufficient background knowledge for further studies of many-body physics, including a short resume of complex analysis (residue calculus).

Learning Objectives

  • Use second quantization
  • Derive correlation functions in linear response
  • Use Wick’s Theorem to factorize higher order Green’s functions
  • Draw and understand Feynman diagrams
  • Use the equation of motion method to determine Green’s functions
  • Understand the connection between Green’s functions and excitation energies
  • Understand the RPA theory for screening and plasmons
  • Understand the BCS theory of superconductors

Course Content

The course introduces the basic concepts in many-body theory. The material is based on the text-book “Introduction to quantum field theory in condensed matter physics”, by H. Bruus and K. Flensberg. Furthermore, the needed mathematical techniques are developed. The course will focus on methods based on the Greens function and we will mostly be concerned with the interacting homogeneous electron gas. formalism. A full quantum dynamical description of thermodynamic properties will be a central theme in the course, which is facilitated by the Greens function formalism. Particular themes will be, the ground state energy, screened interactions, plasmons and superconductivity.

Recommended prerequisites

10303/10112, Basic knowledge of solid state physics on the level of Condensed Matter Physics and Nanoscale Materials Physics 10303 and familiarity with quantum mechanics at the level of Advanced Quantum Mechanics 10112.

Teaching Method

Lectures, group work, exercises


This is an advanced course in theoretical many-body physics in the solid state, which is aimed at students on the last part of their Master’s program.

See course in the course database.





13 weeks




DTU Lyngby Campus

Course code 10318
Course type Candidate
Semester start Week 35
Semester end Week 48
Days Thurs 8-12

7.500,00 DKK