Lecture Schedule

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

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