Course syllabus
Symmetry
Period II, autumn semester 2023. Course code TIF310/FYM310, 7.5 hp.
Time slots for oral examination:
Wednesday Jan 10: 9-9.30, 9.45-10.15, 10.30-11, 13-13.30, 13.45-14.15, 14.30-15
Friday Jan 12: 9-9.30, 9.45-10.15, 10.30-11, 13-13.30, 13.45-14.15, 14.30-15
(For the above times I need the third home assignment already by Jan 5).
Monday Jan 15: 9-9.30, 9.45-10.15, 10.30-11, 13-13.30, 13.45-14.15, 14.30-15
Tuesday Jan 16: 9-9.30, 9.45-10.15, 10.30-11, 13-13.30, 13.45-14.15, 14.30-15
Wednesday Jan 17: 9-9.30, 9.45-10.15, 10.30-11, 13-13.30, 13.45-14.15, 14.30-15
Friday Jan 19: 9-9.30, 9.45-10.15, 10.30-11, 13-13.30, 13.45-14.15, 14.30-15
Pair up, book a time by email. Remember to bring your old graded home problems.
Literature:
May be updated during the course. Last updated: Dec. 2, 2021
Recommended additional reading: "Physics from Symmetry" by Jakob Schwichtenberg.
Lecturer:
Martin Cederwall, room O6102, tel. 7723181, martin.cederwall@chalmers.se
Examination
is done with home assignments (3 sets), and an oral examination.
The home assignments will appear here in due time. Deadlines are Nov. 21, Dec. 11 and Jan. 8.
Problem set 1, due Nov. 21
Problem set 2, due Dec. 11
Problem set 3, due Jan. 8
Solutions, in the form of pdf files produced by TeX/LaTeX, can be sent by email or left in a 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
Problem set 2: 2019 2020 2021 2022
Problem set 3: 2020 2021 2022
Lectures:
Mondays (except Dec. 11) 10-12, Wednesdays 10-12 and 13-15. Extra question hour Dec. 7 10.30-12.
- 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).
Week 2:
- Representations of SL(2). Tensors. Space-time symmetries: the Lorentz, Poincaré and conformal algebras and their action on fields.
Week 3:
- Scalar fields. Classical field theory. Action. Scalars, the Klein-Gordon equation.
Week 4:
- Spinors in 3 and 4 dimensions. The Dirac equation. Action. Chirality
Week 5:
- More about simple Lie algebras. SL(3) etc. Roots and weights. Representations.
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