\vspace {2ex}
\contentsline {section}{\tocsection {}{1}{Jan 16, 2007: {Schr\"odinger}\xspace 's equation}}{3}{section.1}
\contentsline {subsection}{\tocsubsection {}{1.1}{Questions}}{3}{subsection.1.1}
\contentsline {subsection}{\tocsubsection {}{1.2}{Motivating geometric quantization}}{5}{subsection.1.2}
\vspace {2ex}
\contentsline {section}{\tocsection {}{2}{Jan 23, 2007: Categorification}}{7}{section.2}
\contentsline {subsection}{\tocsubsection {}{2.1}{A secret functor}}{7}{subsection.2.1}
\contentsline {subsection}{\tocsubsection {}{2.2}{Bringing in arbitrary categories}}{8}{subsection.2.2}
\vspace {2ex}
\contentsline {section}{\tocsection {}{3}{Jan 30, 2007: Physics is rigged!}}{10}{section.3}
\contentsline {subsection}{\tocsubsection {}{3.1}{The analogous viewpoints}}{10}{subsection.3.1}
\contentsline {subsection}{\tocsubsection {}{3.2}{Switching between the classical and quantum viewpoints}}{10}{subsection.3.2}
\contentsline {subsection}{\tocsubsection {}{3.3}{Wick rotation and a spring in imaginary time (revisited)}}{12}{subsection.3.3}
\vspace {2ex}
\contentsline {section}{\tocsection {}{4}{Jan 23, 2007: Statistical mechanics and deformation of rigs}}{13}{section.4}
\contentsline {subsection}{\tocsubsection {}{4.1}{Statistical mechanics ``quantizes" strings}}{13}{subsection.4.1}
\contentsline {subsection}{\tocsubsection {}{4.2}{A family of rigs via the Boltzmann map}}{14}{subsection.4.2}
\contentsline {subsection}{\tocsubsection {}{4.3}{The analogous situation for quantization}}{15}{subsection.4.3}
\vspace {2ex}
\contentsline {section}{\tocsection {}{5}{Feb 13, 2007: An example of path integral quantization - I}}{16}{section.5}
\contentsline {subsection}{\tocsubsection {}{5.1}{Example: free particle on the real line}}{16}{subsection.5.1}
\contentsline {subsection}{\tocsubsection {}{5.2}{Doing the math}}{17}{subsection.5.2}
\vspace {2ex}
\contentsline {section}{\tocsection {}{6}{Feb 20, 2007: An example of path integral quantization - II}}{20}{section.6}
\contentsline {subsection}{\tocsubsection {}{6.1}{Time-evolution operators}}{20}{subsection.6.1}
\contentsline {subsection}{\tocsubsection {}{6.2}{Bringing in the Hamiltonian}}{21}{subsection.6.2}
\contentsline {subsection}{\tocsubsection {}{6.3}{Computing the normalizing factors}}{22}{subsection.6.3}
\vspace {2ex}
\contentsline {section}{\tocsection {}{7}{Feb 27, 2007: More examples of path integrals}}{25}{section.7}
\contentsline {subsection}{\tocsubsection {}{7.1}{A potential problem}}{25}{subsection.7.1}
\contentsline {subsection}{\tocsubsection {}{7.2}{The Lie-Trotter Theorem and self-adjoint operators}}{26}{subsection.7.2}
\contentsline {subsection}{\tocsubsection {}{7.3}{Generalization to complete Riemannian manifolds}}{27}{subsection.7.3}
\contentsline {subsection}{\tocsubsection {}{7.4}{Back to the general picture}}{27}{subsection.7.4}
\contentsline {subsection}{\tocsubsection {}{7.5}{Digression of the day: Cauchy surfaces}}{28}{subsection.7.5}
\vspace {2ex}
\contentsline {section}{\tocsection {}{8}{Mar 6, 2007: Hilbert spaces and operator algebras from categories}}{29}{section.8}
\contentsline {subsection}{\tocsubsection {}{8.1}{(Pre-)Hilbert spaces from categories}}{29}{subsection.8.1}
\contentsline {subsection}{\tocsubsection {}{8.2}{Operators and multiplying them}}{32}{subsection.8.2}
\vspace {2ex}
\contentsline {section}{\tocsection {}{9}{Mar 13, 2007: The big picture}}{33}{section.9}
\contentsline {subsection}{\tocsubsection {}{9.1}{The case of finite categories}}{33}{subsection.9.1}
\contentsline {subsection}{\tocsubsection {}{9.2}{Example: particle on a line}}{33}{subsection.9.2}
\contentsline {subsection}{\tocsubsection {}{9.3}{From particles to strings}}{34}{subsection.9.3}
\contentsline {subsection}{\tocsubsection {}{9.4}{Digression on torsors}}{35}{subsection.9.4}