\BOOKMARK [1][-]{section.1}{1. Jan 16, 2007: Schr\366dinger's equation}{} \BOOKMARK [2][-]{subsection.1.1}{1.1. Questions}{section.1} \BOOKMARK [2][-]{subsection.1.2}{1.2. Motivating geometric quantization}{section.1} \BOOKMARK [1][-]{section.2}{2. Jan 23, 2007: Categorification}{} \BOOKMARK [2][-]{subsection.2.1}{2.1. A secret functor}{section.2} \BOOKMARK [2][-]{subsection.2.2}{2.2. Bringing in arbitrary categories}{section.2} \BOOKMARK [1][-]{section.3}{3. Jan 30, 2007: Physics is rigged!}{} \BOOKMARK [2][-]{subsection.3.1}{3.1. The analogous viewpoints}{section.3} \BOOKMARK [2][-]{subsection.3.2}{3.2. Switching between the classical and quantum viewpoints}{section.3} \BOOKMARK [2][-]{subsection.3.3}{3.3. Wick rotation and a spring in imaginary time \(revisited\)}{section.3} \BOOKMARK [1][-]{section.4}{4. Jan 23, 2007: Statistical mechanics and deformation of rigs}{} \BOOKMARK [2][-]{subsection.4.1}{4.1. Statistical mechanics ``quantizes" strings}{section.4} \BOOKMARK [2][-]{subsection.4.2}{4.2. A family of rigs via the Boltzmann map}{section.4} \BOOKMARK [2][-]{subsection.4.3}{4.3. The analogous situation for quantization}{section.4} \BOOKMARK [1][-]{section.5}{5. Feb 13, 2007: An example of path integral quantization - I}{} \BOOKMARK [2][-]{subsection.5.1}{5.1. Example: free particle on the real line}{section.5} \BOOKMARK [2][-]{subsection.5.2}{5.2. Doing the math}{section.5} \BOOKMARK [1][-]{section.6}{6. Feb 20, 2007: An example of path integral quantization - II}{} \BOOKMARK [2][-]{subsection.6.1}{6.1. Time-evolution operators}{section.6} \BOOKMARK [2][-]{subsection.6.2}{6.2. Bringing in the Hamiltonian}{section.6} \BOOKMARK [2][-]{subsection.6.3}{6.3. Computing the normalizing factors}{section.6} \BOOKMARK [1][-]{section.7}{7. Feb 27, 2007: More examples of path integrals}{} \BOOKMARK [2][-]{subsection.7.1}{7.1. A potential problem}{section.7} \BOOKMARK [2][-]{subsection.7.2}{7.2. The Lie-Trotter Theorem and self-adjoint operators}{section.7} \BOOKMARK [2][-]{subsection.7.3}{7.3. Generalization to complete Riemannian manifolds}{section.7} \BOOKMARK [2][-]{subsection.7.4}{7.4. Back to the general picture}{section.7} \BOOKMARK [2][-]{subsection.7.5}{7.5. Digression of the day: Cauchy surfaces}{section.7} \BOOKMARK [1][-]{section.8}{8. Mar 6, 2007: Hilbert spaces and operator algebras from categories}{} \BOOKMARK [2][-]{subsection.8.1}{8.1. \(Pre-\)Hilbert spaces from categories}{section.8} \BOOKMARK [2][-]{subsection.8.2}{8.2. Operators and multiplying them}{section.8} \BOOKMARK [1][-]{section.9}{9. Mar 13, 2007: The big picture}{} \BOOKMARK [2][-]{subsection.9.1}{9.1. The case of finite categories}{section.9} \BOOKMARK [2][-]{subsection.9.2}{9.2. Example: particle on a line}{section.9} \BOOKMARK [2][-]{subsection.9.3}{9.3. From particles to strings}{section.9} \BOOKMARK [2][-]{subsection.9.4}{9.4. Digression on torsors}{section.9}