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FSH3312 Symmetries in Physial Systems 7.5 credits

About course offering

For course offering

Spring 2024 Start 16 Jan 2024 programme students

Target group

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Part of programme

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P3 (7.5 hp)


16 Jan 2024
15 Mar 2024

Pace of study


Form of study

Normal Daytime

Language of instruction


Course location


Number of places

Places are not limited

Planned modular schedule


For course offering

Spring 2024 Start 16 Jan 2024 programme students

Application code



For course offering

Spring 2024 Start 16 Jan 2024 programme students


Chong Qi


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Course coordinator

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Headings with content from the Course syllabus FSH3312 (Spring 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Symmetry and conservation laws

Groups and group representations

Point groups

Permutation Groups

Lie Groups and Lie Algebras

Unitary Groups

Real Orthogonal Groups

The Symplectic Groups

Theory of identical particles

Angular momentum

SU(N) group in nuclear and particle physics

Coefficient of fractional parentage and seniority 

Isospin symmetry

Spin and pseudospin symmetry in nuclear and relativistic systems

Intended learning outcomes

The main aim of the course is to understand the basic concepts in symmetry principles and group theories and their mathematical formalisms. On completion of the course, the students will be able to apply them to analyze the symmetry properties of complex quantum physical systems including atoms, nuclei and elementary particles. They should also be able to analyse both discrete and continuous symmetries of physical systems using group theory. In particular they should be able to decompose a representation into its irreducible representations. The students will also be able to identify approximate symmetries including isospin and pseudospin and understand their limitations.

Literature and preparations

Specific prerequisites

Admitted to PhD studies in Physics, Biological Physics, or related fields of study.

Recommended prerequisites

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J.P. Elliott and P.G. Dawber, Symmetry in Physics (Volume 1 & 2), Oxford and own lecture notes.

Examination and completion

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

Grading scale

P, F


  • SEM1 - Seminars, 7.5 credits, grading scale: 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

To pass the course the students should give 1-2 open seminars on the subject and hand in a study report. In both cases the students should demonstrate that they have obtained good understanding of the subject and be able to apply their knowledge to practial problems and answer the questions and comments raised by the teacher and other students in a proper way. 

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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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 room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

Main field of study

This course does not belong to any Main field of study.

Education cycle

Third cycle

Add-on studies

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Chong Qi

Postgraduate course

Postgraduate courses at SCI/Physics