Undergraduate Seminar

Following the success of last semester's undergraduate seminar on Coxeter groups and Hecke algebras, we will be running another undergraduate seminar this semester on a slightly different theme: Lie Groups in Physics. The goal of the seminar is to help bridge the gap between pure mathematics and (mathematical) physics, both pedagogically and socially. As such, we welcome students from both the mathematics and physics cohorts from 2nd year onwards, though the talks will be aimed at the 3rd year level. The seminar should (hopefully!) be of interest to students who have studied or are studying Algebra, Quantum Physics/Systems, Methods of Mathematical Physics, Electrodynamics, Geometry, Theoretical Physics, and so on. Talks will be for 100 minutes with a break in the middle. Participants will prepare their presentations under the guidance of one expert or another, and give a practice talk in advance. Great emphasis is put on clear and compelling exposition.

This seminar is coorganized by Anas Rahman, Matthew Spong, Adrian Putra, Gufang Zhao, and Srivatsa Badariprasad. Feel free to contact either of them or Nora Ganter for further details.

To be put on the email list for this seminar, contact aarahman@student.unimelb.edu.au

The seminar will be meeting weekly throughout the semester on Mondays 12:00 to 2:00 in room 107, Peter Hall Building.

Topics are as follows (subject to change).

Week Date Topics Speaker
2 5th August Representations of Groups; [BD] Sections 2.1 to 2.2, and organisation. Anas Rahman
3 12th August An Introduction to Lie Groups; [BD] Sections 1.1 and 1.3 Matthew Spong
4 19th August Clifford Algebras; [BD] Section 1.6, pp.54-57 Spencer Wong
5 26th August Pin and Spin Groups; [BD] Section 1.6, pp.58-62, Notes by Jonah Jonah Nelson
6 2nd September Representations of Some Famous Lie Groups; [BD] Section 1.6, pg.61 and Section 2.5 Brendan Wallis
7 9th September The Special Clifford Algebra and Ancillaries; [PS] Notations and Conventions Gufang Zhao, Anas Rahman
8 16th September Lagrangian Field Theory and Noether's Theorem; [PS] Section 2.1 to 2.2, [DK] Section 6.2 Alexei Sopov
9 23rd September The Lorentz Group and Klein-Gordon Equation; [PS] Section 3.1, [JS] Section 3.7, Notes by Brae Brae Vaughan-Hankinson
Break 30th September Midsemester break
10 7th October The Dirac Algebra and Equation; [PS] Section 3.2, [DS] Sections 1.1 to 1.3, and 3.1 Jackson Godfrey
11 14th October The Weyl, Dirac, and Majorana Spinors; [PS] Section 3.2, [JS] Sections 3.7 and 6.3 Adrian Putra
References

Guideline:

[BD] Brocker, Dieck: Representations of Compact Lie Groups

[PS] Peskin, Schroeder: An Introduction to Quantum Field Theory

Supplementary:

[DK] Dorey, Kirklin: Symmetries, Fields and Particles

[JS] J. Schwichtenberg: Physics from Symmetry

[DS] D. Shirokov: Clifford Algebras and Their Applications to Lie Groups and Spinors, arXiv: 1709.06608