Quantum Gravity Seminar - Winter 2001
This session of the Quantum Gravity Seminar
continued exploring the
themes introduced in the Fall 2000 session: quantum field theory and diagrammatic methods
I started out writing up notes in the same style as in the
fall: a kind of story featuring a Wizard and his Acolytes.
Unfortunately I ran out of energy right when the story
part of the story was getting really interesting.
As far as physics goes, the course has two "tracks":
Here are the notes:
Track 1 is about topological quantum field theories, starting
with the definition and working up to the classification of
2d TQFTs and their construction from lattice field theories.
Track 2 is about quantization of gauge field theories, focusing
on the simple example of the vacuum Maxwell equations in 2
dimensions - on spacetimes of arbitrary topology. At the end
we begin to see how this generalizes to 2d Yang-Mills theory.
Week 11, Track 1
Week 11, Track 2
Week 12, Track 1
Week 12, Track 2
Week 13, Track 1
Week 13, Track 2
Week 14, Track 1
Week 14, Track 2
Week 15, Track 1
Week 15, Track 2
Week 16, Track 1
Week 16, Track 2
Week 17, Track 1
Week 17, Track 2
Álvarez wrote up notes in the
form of a more traditional math/physics textbook. The current
draft is available here:
You may also want to refer to this supplement, on category theory:
We hope to eventually combine all these notes in a
single book, but we all begin more projects more than
If you want to continue learning about these subjects, try the
Spring 2001 session,
where we talked about quantum groups and the Turaev-Viro model.
© 2001 John Baez