From this page you can download copies of my handwritten notes from John Baez's "Quantum Gravity Seminar." The topic of the Quantum Gravity Seminar varies from one quarter to the next, but the 2003-2004 academic year was spent entirely on this series, "Quantization & Categorification." All of these notes, plus notes from other quarters in the seminar, are also available from John's QG page.
I took these notes in real time, during the seminar, and then usually fixed them up a bit before scanning them in. Fortunately John makes a point of being easy to take notes from, which made my task considerably easier than it would have been in most lectures. The notes are a mixture of what John wrote on the board during the seminar, what he said but didn't write down, and sometimes whatever I (mis)interpreted him to be saying! If you discover any errors in these notes, please email me and I'll try to correct them (the old fashioned way, using correction fluid) and rescan the pages. We are keeping lists of errors that haven't been fixed yet, for fall, winter and spring sessions.
There is also an INDEX to these notes, which was created by Mike Stay. The page numbers in the index are prefixed by an "f" for Fall 2003 or "w" for Winter 2004 notes. Someday, some ambitious person might expand the index to include the notes from Spring quarter 2004 as well.
Below are the notes from the Fall 2003 quarter. You can get them as a single (rather large) pdf file:
Complete Notes for Fall 2003 quarter.
These notes © 2003 John Baez and Derek Wise
Week 1 - Review of structure types. This quarter's plan. Fibonacci numbers.
Week 2 - The quantum harmonic oscillator with many degrees of freedom: counting states of a given energy.
Week 3 - The quantum harmonic oscillator with many degrees of freedom: a square of functors commuting up to natural isomorphism. (Only one lecture this week, since Danny Stevenson spoke about gerbes on Thursday.)
Week 4 - Violin string theory: quantizing the open string with Dirichlet boundary conditions.
Week 5 - Two roles of generating functions in quantum theory: as states of the harmonic oscillator, and as partition functions. Partition functions in classical and quantum statistical mechanics.
Week 6 - Generating functions from partition functions: the analogy between thermodynamic systems and structure types. Groupoids as "sets with fractional cardinality". How to evaluate a structure type at a set and get a groupoid.
Week 7 - Applying the structure type F to the set Z and getting the groupoid of "F-structured, Z-colored sets": examples. Categorified hyperbolic trigonometry. Half-colored sets, double factorials, hypercubes and the square root of e.
Week 8 - Applying a structure type F to a groupoid Z and getting a groupoid F(Z) - a categorified version of evaluating a power series at a real number and getting a real number. The necessary technology: taking the weak quotient of a groupoid by a group acting on it. How to define the weak quotient by a universal property.
Week 9 - How to construct the weak quotient. F(Z) as the groupoid of "F-structured finite sets with elements labelled by objects of the groupoid Z". Examples: the groupoid of "finite sets labelled by k-element sets", which has cardinality e1/k!. The groupoid of "finite sets with elements labelled by finite sets", which has cardinality ee.
Week 10 - Composing structuring types - a categorified version of composing functions given by power series. Examples: the structure type "being a finite set with elements labelled by 2-element sets", which has generating function ez2/2!. Categorified hyperbolic trigonometry, revisited. Exponentiation and connected structures. The need for stuff types.
© 2004 John Baez and Derek Wise
Week 2 - Stuff types and the quantum harmonic oscillator.
Week 3 - Stuff types and their generating functions; Composition of stuff types.
Week 4 - The inner product of stuff types.
Week 5 - Inner product of stuff types: the key example. Stuff operators. Categorifying the annihilation operator.
Week 6 - No lecture notes; John was in France, and Aurora del Rio Cabeza filled in for him, giving two talks on categorical groups.
Week 7 - Perturbation theory for the harmonic oscillator.
Week 8 - Feynman diagrams.
Week 9 - Using Feynman diagrams to compute time evolution for the perturbed harmonic oscillator.
Week 10 - Feynman diagrams involving categorified Wick powers.
© 2004 John Baez and Derek Wise