Course curriculum

  • 1

    Course information

    • Course outline

    • Kevin's introduction
  • 2

    Tutorials

    • Tutorial 1

    • Tutorial 1 solutions

    • Tutorial 1 - alternative justification of commutator definition

    • Tutorial 2

    • Tutorial 2 solutions

    • Tutorial 3

    • Tutorial 3 solutions

    • Tutorial 4

    • Tutorial 4 solutions

    • Tutorial 5

    • Tutorial 5 solutions
  • 3

    Homeworks

    • Homework 1

    • Homework 2
  • 4

    Week 1

    • 1 - Background on Differential Forms

    • 1 - Background on Differential Forms

    • 2 - The de Rham complex

    • 2 - The de Rham complex

    • 3 - The de Rham complex part 2

    • 3 - The de Rham complex part 2

    • 4 - Stokes theorem

    • 4 - Stokes theorem

    • 5 - Gauge Fields

    • 5 - Gauge Fields

    • 6 - Large Gauge Transformations

    • 6 - Large Gauge Transformations

    • 7 - Wilson Lines

    • 7 - Wilson Lines

    • 8 - Wilson Lines part 2

    • 8 - Wilson Lines part 2

    • Week 1 survey
  • 5

    Week 2

    • 9 - Field strength and Wilson lines

    • 9 - Field strength and Wilson lines

    • 10 - Wilson lines in Chern-Simons

    • 10 - Wilson lines in Chern-Simons

    • 11 - The Chern-Simons propagator

    • 11 - The Chern-Simons propagator

    • 12 - The propagator part 2

    • 12 - The propagator part 2

    • 13 - The propagator part 3

    • 13 - The propagator part 3
  • 6

    Week 3

    • 14 - More on the linking number

    • 14 - More on the linking number

    • 15 - Feynman diagrams with Wilson lines

    • 15 - Feynman diagrams with Wilson lines

    • 16 - The Jones polynomial

    • 16 - The Jones polynomial

    • 17 - Skein relations

    • 17 - Skein relations
  • 7

    Week 4

    • 18 - The phase space

    • 18 - The phase space

    • 19 - Poisson bracket on the phase space

    • 19 - Poisson bracket on the phase space

    • 20 - The Hilbert space of Chern-Simons

    • 20 - The Hilbert space of Chern-Simons

    • 21 - More on the Hilbert space

    • 21 - More on the Hilbert space

    • 22 - Geometric quantization

    • 22 - Geometric quantization
  • 8

    Week 5

    • 23 - 2d CFTs and Chern- Simons

    • 23 - 2d CFTs and Chern- Simons

    • 24 - Boundary conditions

    • 24 - Boundary conditions

    • 25 - Chern-Simons and the free boson

    • 25 - Chern-Simons and the free boson

    • 26 - More on boundary OPEs

    • 26 - More on boundary OPEs

    • 27 - Kac-Moody algebras

    • 27 - Kac-Moody algebras