Lecture Schedule

I anticipate that we will have about 42-45 lectures during the semester.

1. July 30, 2008: Review of classical mechanics: Principle of least action; Calculus of variations aka Functional calculus.
2. July 31, 2008: Review of classical mechanics: Principle of least action (contd); What is CFT? Assignment 1 on classical mechanics handed out.
3. Aug. 1, 2008: Invariance of Newton's equations: The Galilean group; Rewriting Maxwell's equations (ME) in Gaussian units as a prelude to studying its invariance.
4. Aug. 6, 2008
5. Aug. 7, 2008
6. Aug. 13, 2008
7. Aug. 14, 2008 Elements of group theory: Matrix Groups — orthogonal, unitary and symplectic groups. Finite Groups.
8. Aug. 20, 2008 Finite groups: examples at low orders, cyclic groups, the permutation group.
9. Aug. 21, 2008 Equivalence relations and partitions of sets, cosets, examples, normal subgroups, simple groups and their classification.
10. Aug. 22, 2008 Lagrangians in classical field theory: Ingredients (fields, locality of interactions, causality, symmetries); Lagrangian densities.
11. Aug. 27, 2008 Obtaining a relativistic Lagrangian for a massive real scalar field, Klein-Gordon equation
12. Aug. 28, 2008 Real scalar field with arbitrary potential; Hamiltonian density; conditions for time-independent, finite-energy solutions; the ground state.
13. Aug. 29, 2008 Discussion on assignments 1 and 2.
14. Sept. 3, 2008 Discussion on assignments continued.
15. Sept. 4, 2008 Noether's theorem: Obtaining the energy-momentum (stress) tensor as a Noether charge.
16. Sept. 5, 2008 Green function for the Klein-Gordon equation (with sources).
17. Sept. 10, 2008 Green function (contd.)
18. Sept. 11, 2008 Discussion on assignment 4/Lecture on the kink soliton.
19. Sept. 17, 2008
20. Sept. 18, 2008
21. Sept. 19, 2008 Noether's Theorem (general discussion + applications)
22. Sept. 24, 2008 Noether's Theorem (contd)
23. Sept. 25, 2008 Lie Algebras
24. Sept. 26, 2008 Lie Algebras (contd)
25. Oct. 8, 2008 Discussion on assignment 6/Lecture on the energy-momentum tensor, angular momentum of the electromagnetic field; spin angular momentum.
26. Oct. 10, 2008 Goldstone's theorem (background)
27. Oct. 15, 2008 Goldstone's theorem (abelian example)
28. Oct. 16, 2008 Local symmetries, covariant derivatives (the abelian Higgs model/scalar QED)
29. Oct. 17, 2008 Getting around Derrick's Theorem: Vortices in the abelian Higgs model and type-II superconductors.
30. Oct. 18, 2008 Vortices; topological conservation laws; fundamental groups: $\Pi_1(S^1)$, $\Pi_n(X)$, ..
31. Oct. 22, 2008 Quiz
32. Oct. 23, 2008 Discussion of Quiz paper and problem set 7.
33. Oct. 24, 2008 Vortices as solutions of first-order equations (the Bogomolnyi limit)
34. Oct. 29, 2008 Non-abelian Goldstone's theorem; the coset $G/H$ and its parametrization of fluctuations.
35. Oct. 30, 2008 Non-abelian gauge theories: Recap on representation theory of Lie groups and algebras: fundamental and adjoint representations; unitary irreducible representations; Lagrangian densities with global continuous symmetries
36. Oct. 31, 2008 Non-abelian gauge theories: (contd.) From global symmetries to local symmetries via the covariant derivative; non-abelian gauge fields and their transformation under local global symmetries (aka local gauge transformations); the field strength and the kinetic term for the non-abelian gauge fields. Comparison with the abelian example.
37. Nov. 5, 2008 Non-abelian Higgs mechanism; the electro-weak symmetry breaking: $SU(2)\times U(1)_Y \rightarrow U(1)_{EM}$; the Weinberg angle.
38. Nov. 6, 2008 Organizing the particle zoo: the eight-fold way(Gell-Mann); Estimating masses of mesons using chiral symmetry breaking (Nambu)
39. Nov. 7, 2008 The Standard Model: Colour and the strong force;confinement; From quarks to mesons and baryons;
40. Nov. 12, 2008 Dirac Monopole, Charge quantization.
41. Nov. 14, 2008 Monopoles and Dyons: the 't Hooft-Polyakov monopole in the Prasad-Sommerfeld limit; the Julia-Zee dyon;
42. Nov. 28, 2008 Final Examination
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