The  seeker

Michael Stone's Physics Page

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.

Short Notes and Essays

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.

Mechanics problems and exercises

Annoying golf ball.
A falling chain.
Rocket engine de Laval nozzle: good practice in integration by parts.

Longer Notes

Review of BCS Formalism: Deriving the Magnus effect from the Berry phase.
A review of Torsion and it's effect on the Dirac equation.
Euclidean Dirac Formalism: Anomalies and the Index Theorem.
Anomalies, thermodynamics, and fluid dynamics.