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FSI3210 Many Particle Physics 7.5 credits

The course gives the basis for modern condensed matter theory. Problems are studied that cannot be analyzed by starting from the properties of single atoms in a material, but from collective phenomena like superconductivity, which emerges when a large number of atoms are coupled together. In earlier courses in quantum mechanics, systems with a very small number of particles are treated. In statistical mechanics systems with many non-interacting bosons and fermions are studied. The aim in this course is to introduce a formalism which allows describing systems with a large number of interacting quantum mechanical particles. With the help of this formalism we will consider several collective phenomena in condensed matter systems such as superconductivity, superfluidity and magnetism.

Course offering missing for current semester as well as for previous and coming semesters
Headings with content from the Course syllabus FSI3210 (Spring 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Part 1.

The first part of the course is devoted to explain basic formalism of the many body theory. It starts from the second quantization representation of quantum mechanical operators acting in the Hilbert space of a system consisting of many identical particles. Based on this technique the Green’s functions are introduced and then their analytical properties are discussed. The perturbation theory and Feynman rules are discussed both for the ground state and equilibrium systems at finite temperatures, fermions and bosons. The linear response theory is introduced.

Part 2

During the second part of the course the general formalism will be applied to several examples of collective phenomena in condensed matter systems. The microscopic physics of superconductivity will be discussed in detail. Superfluidity in a weakly interacting Bose gas will be considered. The basic models of magnetism and spin-dependent collective phenomena like Kondo effect and RKKY interaction between magnetic impurities will be introduced.

Intended learning outcomes

After completed course, the PhD student should be able to:

  • use second quantization formulation of quantum field theory.
  • use Green's function technique.
  • use Feynman diagrams.
  • master the theories for the electron gas, superconductivity (BCS theory), and for superfluids.
  • master the theoretical background for magnetism.

Course disposition

No information inserted

Literature and preparations

Specific prerequisites

Good knowledge about all compulsory physics courses and statistical mechanics.

Recommended prerequisites

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Fetter och J. Walecka, Quantum theory of many particle systems, McGraw-Hill 1971.

A. A. Abrikosov, L. P. Gorkov och I. Y. Dzyaloshinskii, Quantum field theoretical methods in statistical physics, Pergamon, 1965.

A. Zagoskin, Quantum theory of many-body systems: techniques and applications, Springer-Verlag, 1998

R. White, Quantum Theory of Magnetism, Springer-Verlag, 2007   

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

P, F


  • TEN1 - Oral exam, 7,5 hp, betygsskala: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Other requirements for final grade

Hand in problems, oral exam.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

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Profile picture Egor Babaev

Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web FSI3210

Offered by


Main field of study

No information inserted

Education cycle

Third cycle

Add-on studies

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Egor Babaev

Postgraduate course

Postgraduate courses at SCI/Physics