TFY4210 - Quantum Theory of Many-Particle Systems


Examination arrangement

Examination arrangement: Written examination
Grade: Letters

Evaluation form Weighting Duration Examination aids Grade deviation
Written examination 100/100 4 hours C

Course content

Klein-Gordon and Dirac equation. Field quantization. Occupation number representation for nonrelativistic fermionic and bosonic many-particle systems. Interacting electron gas. Lattice models for fermions and spins. Spin-wave theory of ferro- and antiferromagnets. Symmetries and conserved quantities. Broken symmetries, Goldstone modes. Green functions. Matsubara formalism. Many-particle perturbation theory and Feynman diagrams. Various applications.

Learning outcome

The course shall give the students an elaboration and more advanced treatment of the material in the courses FY2045/TFY4250 and TFY4205, with applications in atomic physics, relativistic quantum mechanics and condensed matter physics. The students will obtain knowledge of key examples of field theories and lattice models for systems of interacting fermions, bosons, and spins, and learn to use relevant theoretical concepts and methods to analyze various aspects of these models. More specifically, the students will:
- learn about relativistic quantum mechanics (the Klein-Gordon and Dirac equation);
- master the usage of creation and annihilation operators for fermion and boson systems;
- master Fourier and Bogoliubov transformations for diagonalization of quadratic Hamiltonians;
- be introduced to many-particle Green functions and how these are related to various quantities of interest;
- get an introduction to many-particle perturbation theory, including Feynman diagrams;
- acquire knowledge about various other methods, e.g. spin wave theory;
- learn about key concepts, including quasiparticles, order parameters, (broken) symmetries and Goldstone modes.

Learning methods and activities

Lectures and home work problems. All students will go through one of the calculation exercises on the blackboard during the semester, to be allowed to take the exam. The course will be given in English if students on the international master program in physics are attending the course. When lectures and lecture material are in English, the exam may be given in English only.

Compulsory assignments

  • Calculation exercises

Further on evaluation

The re-sit examination (in August) may be changed from written to oral.

Specific conditions

Exam registration requires that class registration is approved in the same semester. Compulsory activities from previous semester may be approved by the department.

Course materials

P. C. Hemmer: Kvantemekanikk (Tapir, 2005), A. L. Fetter and J. D. Walecka: Quantum theory of many-particle systems (Dover, 2003), H. Bruus and K. Flensberg: Many-body quantum theory in condensed matter physics (Oxford, 2004).

Credit reductions

Course code Reduction From To
FY8916 7.5 2017-09-01
SIF4047 7.5


Detailed timetable


Examination arrangement: Written examination

Term Statuskode Evaluation form Weighting Examination aids Date Time Room *
Spring ORD Written examination 100/100 C
  • * The location (room) for a written examination is published 3 days before examination date.
If more than one room is listed, you will find your room at Studentweb.