\vspace {2ex} \contentsline {section}{\tocsection {}{1}{Preface}}{3}{section.1} \vspace {2ex} \contentsline {section}{\tocsection {}{2}{Jan 16, 2007: {Schr\"odinger}\xspace 's equation}}{4}{section.2} \contentsline {subsection}{\tocsubsection {}{2.1}{Questions}}{4}{subsection.2.1} \contentsline {subsection}{\tocsubsection {}{2.2}{Motivating geometric quantization}}{6}{subsection.2.2} \vspace {2ex} \contentsline {section}{\tocsection {}{3}{Jan 23, 2007: Categorification}}{8}{section.3} \contentsline {subsection}{\tocsubsection {}{3.1}{A secret functor}}{8}{subsection.3.1} \contentsline {subsection}{\tocsubsection {}{3.2}{Bringing in arbitrary categories}}{9}{subsection.3.2} \vspace {2ex} \contentsline {section}{\tocsection {}{4}{Jan 30, 2007: Physics is rigged!}}{11}{section.4} \contentsline {subsection}{\tocsubsection {}{4.1}{The analogous viewpoints}}{11}{subsection.4.1} \contentsline {subsection}{\tocsubsection {}{4.2}{Switching between the classical and quantum viewpoints}}{11}{subsection.4.2} \contentsline {subsection}{\tocsubsection {}{4.3}{Wick rotation and a spring in imaginary time (revisited)}}{13}{subsection.4.3} \vspace {2ex} \contentsline {section}{\tocsection {}{5}{Jan 23, 2007: Statistical mechanics and deformation of rigs}}{14}{section.5} \contentsline {subsection}{\tocsubsection {}{5.1}{Statistical mechanics quantizes" strings}}{14}{subsection.5.1} \contentsline {subsection}{\tocsubsection {}{5.2}{A family of rigs via the Boltzmann map}}{15}{subsection.5.2} \contentsline {subsection}{\tocsubsection {}{5.3}{The analogous situation for quantization}}{16}{subsection.5.3} \vspace {2ex} \contentsline {section}{\tocsection {}{6}{Feb 13, 2007: An example of path integral quantization - I}}{18}{section.6} \contentsline {subsection}{\tocsubsection {}{6.1}{Example: free particle on the real line}}{18}{subsection.6.1} \contentsline {subsection}{\tocsubsection {}{6.2}{Doing the math}}{19}{subsection.6.2} \vspace {2ex} \contentsline {section}{\tocsection {}{7}{Feb 20, 2007: An example of path integral quantization - II}}{23}{section.7} \contentsline {subsection}{\tocsubsection {}{7.1}{Time-evolution operators}}{23}{subsection.7.1} \contentsline {subsection}{\tocsubsection {}{7.2}{Bringing in the Hamiltonian}}{24}{subsection.7.2} \contentsline {subsection}{\tocsubsection {}{7.3}{Computing the normalizing factors}}{25}{subsection.7.3} \vspace {2ex} \contentsline {section}{\tocsection {}{8}{Feb 27, 2007: More examples of path integrals}}{28}{section.8} \contentsline {subsection}{\tocsubsection {}{8.1}{A potential problem}}{28}{subsection.8.1} \contentsline {subsection}{\tocsubsection {}{8.2}{The Lie-Trotter Theorem and self-adjoint operators}}{29}{subsection.8.2} \contentsline {subsection}{\tocsubsection {}{8.3}{Generalization to complete Riemannian manifolds}}{30}{subsection.8.3} \contentsline {subsection}{\tocsubsection {}{8.4}{Back to the general picture}}{30}{subsection.8.4} \contentsline {subsection}{\tocsubsection {}{8.5}{Digression of the day: Cauchy surfaces}}{31}{subsection.8.5} \vspace {2ex} \contentsline {section}{\tocsection {}{9}{Mar 6, 2007: Hilbert spaces and operator algebras from categories}}{33}{section.9} \contentsline {subsection}{\tocsubsection {}{9.1}{(Pre-)Hilbert spaces from categories}}{33}{subsection.9.1} \contentsline {subsection}{\tocsubsection {}{9.2}{Operators and multiplying them}}{36}{subsection.9.2} \vspace {2ex} \contentsline {section}{\tocsection {}{10}{Mar 13, 2007: The big picture}}{37}{section.10} \contentsline {subsection}{\tocsubsection {}{10.1}{The case of finite categories}}{37}{subsection.10.1} \contentsline {subsection}{\tocsubsection {}{10.2}{Example: particle on a line}}{37}{subsection.10.2} \contentsline {subsection}{\tocsubsection {}{10.3}{From particles to strings}}{39}{subsection.10.3} \contentsline {subsection}{\tocsubsection {}{10.4}{Digression on torsors}}{40}{subsection.10.4}