Course syllabus

Symmetry
Period II, autumn semester 2025. Course code TIF310/FYM310, 7.5 hp.

 

News:

Nov. 28: Second set of home problems available (below). Old corrected home problems are in a box outside O6102.

Nov. 7: First set of home problems available (below).

Oct. 20: Page under construction.

 

 

Literature:

Lecture notes

May be updated during the course. Last updated: Nov. 17, 2024 (errors in answers to exercises corrected).

(Strongly) recommended additional reading and support: "Physics from Symmetry" by J. Schwichtenberg. This book contains many of the things we do in the course, often with a somewhat lower level of mathematical stringency.
"Group theory in a nutshell for physicists" by A. Zee.

 

Lecturer:

Martin Cederwall, room O6102, tel. 7723181, martin.cederwall@chalmers.se

 

Course representatives:

to appear.

 

Examination

is done with home assignments (3 sets), and an oral examination.

The home assignments will appear here in due time. Deadlines are Nov. 22, Dec. 12 and Jan. 9.

Problem set 1, due Nov. 21

Problem set 2, due Dec. 12

Problem set 3, due Jan. 9

Solutions, in the form of pdf files produced by TeX/LaTeX, can be sent by email or left in a box outside room O6102.

Graded assignments can be found in at box outside room O6102.

The grade is based on the results on the home assignments, where approximate limits are 1/2 of the maximum number of points for grade 3, 2/3 for grade 4 and 5/6 for grade 5. For GU students: 1/2 for G, 3/4 for VG. The maximum number of points is 30 (preliminary, 2 points for each problem).

Oral examination  January.

The oral examination is done in pairs. Its purpose is to see that you are able to answer for what you did in the home assignments.

Old assignments:
Problem set 1: 2019 2020 2021 2022 2023 2024
Problem set 2: 2019 2020 2021 2022 2023 2024
Problem set 3:                2020 2021 2022 2023 2024

 

Schedule from TimeEdit

 

Lectures:

Mondays 10-12, Wednesdays 10-12 and 13-15. Extra question hour Dec. 10 15.15-16.30.

        These lectures are a mix of theory lectures, applications and question hours.
        Typically, Wednesday afternoon will be more oriented towards problem-solving.
        It is advisable to prepare by reading and working through the relevant parts of the lecture notes.
        The teaching takes place live, in the rooms indicated on the schedule.

Plan:

Week 1:

          Linear spaces. Groups, Lie groups, Lie algebras. Representations. SL(2).
          (Chapters 1,2.1-6 in lecture notes)

Week 2:

          Representations of SL(2). Tensors. Space-time symmetries: the Lorentz, Poincaré (and conformal) algebras and their action on fields.
          (2.7,2.14,3.1-3)

Week 3:

          Scalar fields. Classical field theory. Action. Scalars, the Klein-Gordon equation.
          (4.1,5.1-2,6)

Week 4:

          Spinors in 3 and 4 dimensions. The Dirac equation. Action. Chirality. Spinors in arbitrary dimensions,
          (7)

Week 5:

          More about simple Lie algebras. SL(3) etc. Roots and weights. Representations.
          (2.8-12)

Week 6:

          Forms, gauge fields, Yang–Mills theory. Hamiltonian formulation.

Week 7:

          Noether's theorem, conserved charges.

Links:

The Dirac equation by David Tong, Cambridge

Lectures on gauge theory by José Figueroa-O'Farrill, Edinburgh

Introduction to Lie groups and Lie algebras by Alexander Kirillov, Stony Brook