Quantum Gravity Seminar - Winter 2004

Quantization and Categorification

John Baez and Derek Wise

Here are some lecture notes on quantization and categorification. They are a continuation of the Fall 2003 notes. As before, these notes have been written by Derek Wise, based on lectures by John Baez.

In the fall session we talked about how to quantize and then categorify the simplest physical system of all: the harmonic oscillator. Lots of people know how to quantize the harmonic oscillator, but fewer know that if you then categorify it you recover Joyal's theory of "structure types", which is important in combinatorics. This gives a purely combinatorial explanation of the discreteness arising in the quantum harmonic oscillator!

In this quarter we'll generalize this discussion to include quantum field theory, delve deeper into the category theory behind structure types, and introduce "stuff types" - which appear when you categorify the theory of Feynman diagrams.

Besides the lecture notes you can also get homework problems, which contain mini-essays on related topics. You can also get answers to some of these problems. Different answers shed different light on the problems, and some include cool extra stuff!

All of these are PDF files:

Mike Stay has kindly created an index to these notes:

For the continuation of this course, check out the Spring 2004 notes! You can also find links to more references there.

If you discover any errors in the course notes please email me, and we'll try to correct them. We're keeping a list of errors that haven't been fixed yet.

Here's a terse outline of the whole course:

Yet another view of the same material can be found in this paper: If you're interested in structure types and generating functions, you'll also enjoy these books:

You can also download TeX or LaTeX files of the homework problems and some solutions, if for some bizarre reason you want them. However, the authors keep all rights to this work, except when stated otherwise.

© 2004 John Baez and Derek Wise