\BOOKMARK [1][-]{section.1}{1. Preface}{}
\BOOKMARK [1][-]{section.2}{2. Jan 16, 2007: Schr\366dinger's equation}{}
\BOOKMARK [2][-]{subsection.2.1}{2.1. Questions}{section.2}
\BOOKMARK [2][-]{subsection.2.2}{2.2. Motivating geometric quantization}{section.2}
\BOOKMARK [1][-]{section.3}{3. Jan 23, 2007: Categorification}{}
\BOOKMARK [2][-]{subsection.3.1}{3.1. A secret functor}{section.3}
\BOOKMARK [2][-]{subsection.3.2}{3.2. Bringing in arbitrary categories}{section.3}
\BOOKMARK [1][-]{section.4}{4. Jan 30, 2007: Physics is rigged!}{}
\BOOKMARK [2][-]{subsection.4.1}{4.1. The analogous viewpoints}{section.4}
\BOOKMARK [2][-]{subsection.4.2}{4.2. Switching between the classical and quantum viewpoints}{section.4}
\BOOKMARK [2][-]{subsection.4.3}{4.3. Wick rotation and a spring in imaginary time \(revisited\)}{section.4}
\BOOKMARK [1][-]{section.5}{5. Jan 23, 2007: Statistical mechanics and deformation of rigs}{}
\BOOKMARK [2][-]{subsection.5.1}{5.1. Statistical mechanics ``quantizes" strings}{section.5}
\BOOKMARK [2][-]{subsection.5.2}{5.2. A family of rigs via the Boltzmann map}{section.5}
\BOOKMARK [2][-]{subsection.5.3}{5.3. The analogous situation for quantization}{section.5}
\BOOKMARK [1][-]{section.6}{6. Feb 13, 2007: An example of path integral quantization - I}{}
\BOOKMARK [2][-]{subsection.6.1}{6.1. Example: free particle on the real line}{section.6}
\BOOKMARK [2][-]{subsection.6.2}{6.2. Doing the math}{section.6}
\BOOKMARK [1][-]{section.7}{7. Feb 20, 2007: An example of path integral quantization - II}{}
\BOOKMARK [2][-]{subsection.7.1}{7.1. Time-evolution operators}{section.7}
\BOOKMARK [2][-]{subsection.7.2}{7.2. Bringing in the Hamiltonian}{section.7}
\BOOKMARK [2][-]{subsection.7.3}{7.3. Computing the normalizing factors}{section.7}
\BOOKMARK [1][-]{section.8}{8. Feb 27, 2007: More examples of path integrals}{}
\BOOKMARK [2][-]{subsection.8.1}{8.1. A potential problem}{section.8}
\BOOKMARK [2][-]{subsection.8.2}{8.2. The Lie-Trotter Theorem and self-adjoint operators}{section.8}
\BOOKMARK [2][-]{subsection.8.3}{8.3. Generalization to complete Riemannian manifolds}{section.8}
\BOOKMARK [2][-]{subsection.8.4}{8.4. Back to the general picture}{section.8}
\BOOKMARK [2][-]{subsection.8.5}{8.5. Digression of the day: Cauchy surfaces}{section.8}
\BOOKMARK [1][-]{section.9}{9. Mar 6, 2007: Hilbert spaces and operator algebras from categories}{}
\BOOKMARK [2][-]{subsection.9.1}{9.1. \(Pre-\)Hilbert spaces from categories}{section.9}
\BOOKMARK [2][-]{subsection.9.2}{9.2. Operators and multiplying them}{section.9}
\BOOKMARK [1][-]{section.10}{10. Mar 13, 2007: The big picture}{}
\BOOKMARK [2][-]{subsection.10.1}{10.1. The case of finite categories}{section.10}
\BOOKMARK [2][-]{subsection.10.2}{10.2. Example: particle on a line}{section.10}
\BOOKMARK [2][-]{subsection.10.3}{10.3. From particles to strings}{section.10}
\BOOKMARK [2][-]{subsection.10.4}{10.4. Digression on torsors}{section.10}