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SI2215 Symmetries in Physics 7.5 credits

Introductory group theory, symmetry groups to different physical systems, discrete groups, Lie groups, group generators and Liealgebror, matrix groups, representation theory, key symmetries in physics, Lagranges and Hamilton's formulations of classical mechanics, Noethers rate, motion constants and effective potentials, selected specializations related to symmetry regimes in physics, Basic introduction to the theories used as examples.

About course offering

For course offering

Spring 2025 Start 17 Mar 2025 programme students

Target group

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Part of programme

Master's Programme, Engineering Physics, åk 1, TFYA, Conditionally Elective


P4 (7.5 hp)


17 Mar 2025
2 Jun 2025

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 2025 Start 17 Mar 2025 programme students

Application code



For course offering

Spring 2025 Start 17 Mar 2025 programme students


Sandhya Choubey (


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Course coordinator

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Headings with content from the Course syllabus SI2215 (Autumn 2023–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Introductory group theory, examples of important symmetries in physics, discrete groups, homomorphisms, isomorphisms, representation theory, Lie groups and Lie algebras, representations of simple Lie algebras, unitary and orthogonal groups, roots, weights and Dynkin diagrams, tensor methods, Young tables, selected examples where symmetries are used in physics, applications of group theory in physics.

Intended learning outcomes

After completing the course, a student should be able to:

  1. Analyze physical systems using group theory and symmetry considerations
  2. Using symmetry arguments to limit the form of various physical quantities
  3. Use Lie groups and Lie algebras and construct root and weight diagrams
  4. Analyze the properties of physical systems under space-time transformations and apply it to quantum field theory and gauge theory

Literature and preparations

Specific prerequisites

English B/English 6

Knowledge in physics corresponding to SI1155 Theoretical physics.

Recommended prerequisites

Knowledge corresponding to the first two years courses in mathematics and vector analysis, mathematical methods in physics and theoretical physics


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Examination and completion

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

Grading scale

A, B, C, D, E, FX, F


  • TENA - Written exam, 7.5 credits, grading scale: A, B, C, D, E, FX, 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.

The course is examined through an examination (TENA) which can be written or oral.

TENA - exam/examination, 7.5 credits, grading scale: A, B, C, D, E, Fx, F

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


Education cycle

Second cycle

Add-on studies

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Sandhya Choubey (

Transitional regulations

If a student has passed previous course modules in the course, these can be used to reduce the student's examination requirements for the TENA course module. The examiner decides in each individual case how the reduction of the examination requirements can take place. The transitional provisions apply until VT 2025.

Supplementary information

The course is examined through two examinations, which may be oral or written.At the written exam, both courses can be examined at the same time.
The course can not be included in the exam together with SI1142 or SI2360