These notes are a byproduct of various research projects. They were mostly written for myself as reminder of adopted conventions, and as versions of derivations that are standard but hard to find in the literature. I have put them up here in the hope that they might be useful to others. Please bear in mind that they were meant as reminders for me, and may be rather terse in places.
Bose Bogoliubov transformations and Williamson's theorem.
Fractional charge and Dirac eigenstates.
Variable frequency oscillator and squeezed states.
Kahler potential and Berry Phase.
Is the Gouy/Maslov phase a Berry Phase?
Geodesic co-ordinates and curvature.
A solvable toy model for spectral flow and anomalies.
Schwinger's 3-j symbol and combinatorics.
Laplacians on and their eigenfunctions on Euclidean AdS_2 --- otherwise known as Lobachevski space.
Conformally covariant Laplacian and improved energy-momentum tensor
Waves in Rindler space and Unruh radiation.
Bosonization on Torus and QHE chiral edge modes.
Useful theta function identities.
Charge density waves, Fractional Charge and Anomalies.
Equivariant cohomology for physicists.
Energy-momentum Ward identies, Lie derivatives, and spinors.