Groups And Symmetries (December Exam) PHYS5051

  • Academic Session: 2023-24
  • School: School of Physics and Astronomy
  • Credits: 10
  • Level: Level 5 (SCQF level 11)
  • Typically Offered: Semester 1
  • Available to Visiting Students: Yes

Short Description

This course will introduce the fundamentals of group theory and how this relates to the principle of symmetry. These ideas will be applied to solid state physics and particle physics. Students of this course will not be present for the April/May exam diet.


Typically 2 lectures per week

Requirements of Entry




Excluded Courses







Unseen examination.



In accordance with the University's Code of Assessment reassessments are normally set for all courses which do not contribute to the honours classifications. For non honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students, and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions are listed below in this box.

Main Assessment In: December

Are reassessment opportunities available for all summative assessments? No

Reassessment of the main diet examination is normally available for students on PGT degree programmes if they do not achieve an overall course grade of C3 at their first attempt.


Reassessment of the main diet examination is not normally available for students on Honours degree programmes.


Reassessment is not normally allowed, for practical reasons, for any other assessed components of coursework.

Course Aims

The aims of this course are:

(1) To introduce the fundamental principles of group theory from a physics perspective.

(2) To discuss representation theory and irreducible representations, and their relevance to physics.

(3) To describe simple examples of discrete groups that have application in solid state physics.

(4) To describe simple examples of continuous groups that have application in particle physics.

(5) To describe the Lorentz and Poincaré groups and their use in physics.

Intended Learning Outcomes of Course

By the end of this course students will be able to:


(1) Define and describe various discrete and continuous groups

(2) Explain the difference between Abelian and non-Abelian groups

(3) Explain the difference between reducible and irreducible representations of a group

(4) Specify the generators of the SU(2), SO(3), SU(3), Lorentz and Poincaré groups and the elements of the corresponding Lie groups

(5) Construct representations of the SU(N), SO(N) groups

(6) Explain the meaning of Clebsch-Gordan coefficients and use them in physics applications

(7) Explain the classification of fundamental and composite particles in the standard model of particle physics in terms of irreducible representations of the Lorentz group.

Minimum Requirement for Award of Credits

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.