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 students shall be given an advanced and complementary fulfillment of the courses FY2045/TFY4250 and TFY4205, with applications in atomic physics, relativistic quantum mechanics and solid state physics. The students will obtain knowledge of key examples of field theories and lattice models for systems of interacting bosons, fermions, 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 classical field theory, including the connection between continuous symmetries and conservation laws;
- learn to analyze relativistic wave equations with and without an external field;
- learn about quantization of relativistic and nonrelativistic field theories;
- master the usage of creation and annihilation operators for boson and fermion systems;
- be introduced to Green's functions and how these are related to various quantities of interest;
- get an introduction to manybody perturbation theory, including Feynman diagrams and renormalization;
- master Bogoliubov and Fourier transformations for diagonalization of quadratic Hamtilton operators;
- acquire knowledge about various other methods, e.g., spin wave theory and effective potentials;
- learn about key concepts including quasi particles, order parameters, spontaneous 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. A re-sit examination may be changed from written to oral.

Compulsory assignments

• Calculation exercises

Recommended previous knowledge

The courses FY2045/TFY4250 and TFY4205 or equivalent.

Required previous knowledge

None.

Course materials

P. C. Hemmer: Kvantemekanikk,
A. L. Fetter og J. D. Walecka: Quantum theory of many-particle systems
(Dover Publications, Mineola, New York 2003 paperback)
J. O. Andersen, Lecture Notes.

Credit reductions