Notes

Below are some sets of notes I have written over the past few years. They are in general short, unoriginal, and intended as first reads for the topics in question.

• Bubbles of nothing in the Kaluza-Klein Vacuum (link)

A review of Witten's classic construction of the bubble of nothing spacetime, a discussion of instantons, a rumination on higher dimensional generalizations.

• Can the Standard Model arise from Kaluza-Klein compactification alone? (link)

Obtaining gauge symmetry from diffeomorphism invariance, analysis on homogenous spaces, index theorems for Dirac operators on compact spaces.

• Path integrals for the symmetric double well (link)

Generalities with the path integral, evaluation of fluctuation determinants, interacting fluctuation expansions, degeneracy splitting by instantons in the dilute gas approximation.

• Unitarity theorems for black hole evolution (link)

Page's theorem 'proven' two ways, measures and metrics on the space of mixed quantum states, the Hayden-Preskill thought experiment, comments on black hole complementarity and matrix ensembles.