Physics 521 Group Theory

Announcements

If you are following this course, please bookmark and check this page regularly for announcements.

Please work on Tutorial I
which is due on Monday, February 2, 2026, at 23:59 PM.

Lectures will occur on Monday, Wednesday and Friday at 11:00AM in Henn 301.
January 5 - April 10, 2026.

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This will be an in-person lecture style course. I will also do my best to make it accessible remotely by livestreaming and recording lectures using zoom and posting the recordings below.
From time to time it may be necessary to present the class online at very short notice.
In-person students should make sure that they have the appropriate wifi access,
computer equipment and working access to zoom.
The zoom link is

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https://ubc.zoom.us/j/63549074883?pwd=y7WZbaMe2YpYs0cjcolQO1mUMRyt40.1
Meeting ID: 635 4907 4883
Passcode: 424181

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This course will be an elementary introduction to group theory
including both discrete and Lie groups in language
which should be familiar to physicists.

Prerequisite: The official prerequisite for the course is Physics 500.
However, if you do not have PHYS 500, a background in quantum mechanics
and a working knowledge of linear algebra (matrices, similarity transformations, eigenvalues,
determinants, etc.) are all that you really need.

This course should be accessible to undergraduate students in the upper years of physics or math programs and in the past a number of undergraduate student have taken this course and have done very well. If you are an undergraduate and you are interested in this course,
please talk to me before you sign up.

Evaluation:

Assignments: 60%
Midterm Exam: 15%
Final Exam: 25%

Teaching assistant
The TA is ....

Recorded Lectures
Definition of a group and some examples, January 5, 2026
O(3) and SO(3), January 7, 2026
Representations as group Homomorphisms Jan9, 2026
Finite discrete groups, multiplication table, presentation, Jan12, 2026
Representations and degeneracy of quantum states Jan14, 2026
Cayley's Theorem and the Dihedral groups, January 16, 2026
The Symmetric Groups, January 19, 2026
Conjugacy classes, January 21, 2026
Cosets, January 23, 2026
Mashke's theorem January 26, 2026
Mashke's theorem and Shur's first lemma January 26, 2026
Shur's second and third lemmas January 28, 2026
Brief review and the example of D3 January 30, 2026

Recorded Lectures from 2024 (the current course might differ from that one in important ways):
Definition of a group and some examples, January 8, 2024
O(3) and the Schroedinger equation, January 12, 2024
Representations, January 15, 2024
Properties of group homomorphisms January 17, 2024
The example of the dihedral group January 19, 2024
Conjugacy as an equivalence relation January 22, 2024
Conjugacy classes of the symmetric group January 24, 2024
Cosets January 26, 2024
Mashke's Theorem January 29, 2024
Schur's First and Second Lemmas January 31, 2024
Schur's Third Lemma February 5, 2024
Character of SO(3) February 7, 2024
Crystal Field Splitting February 9, 2024
The Regular Representation February 12, 2024
Proof of character vector completeness February 14, 2024
Lie Groups and Lie Algebras February 26, 2024
The group manifolds of SU(2) and SO(3) February 28, 2024
All finite dimensional representations of su(2) March 4, 2024
Cartan subalgebra March 8, 2024
Weyl-Cartan basis, geometry of root systems March 11, 2024
Simple roots March 13, 2024
su(3) March 18, 2024
su(3)cont March 20, 2024
so(2n) March 22, 2024
so(2n+1), spinors March 25, 2024
The classification theorem March 27, 2024