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Explicit Baker–Campbell–Hausdorff–Dynkin formula for Spacetime via Geometric Algebra · arχiv
In brief. In \(≤4\) dimensions, there’s a simple formula for the bivector \(σ_3\) in terms of bivectors \(σ_1\) and \(σ_2\) such that \(e^{σ_1}e^{σ_2} = ±e^{σ_3}\). Abstract. We present a compact Baker–Campbell–Hausdorff–Dynkin formula for the composition of Lorentz transformations \(e^{σ_i}\) in the spin representation (a.k.a. Lorentz rotors) in terms of their... Read more
Mathematical One-liners
A collection of succinct but wonderfully satisfying mathematical results. Read more
An Overview of the Strong CP Problem and Axion Cosmology · PDF
Literature review supervised by Dr. Jenni Adams at the University of Canterbury. I wanted to learn more about particle physics after my Bachelor’s, so a year of part-time study culminated in this literature review. I learned basic classical (and a little quantum) field theory, and read about the “strong \(CP\)... Read more
The Many Faces of Stokes’ Theorem
Interactively tabulate the special cases of Stokes’ theorem, \( \int_Ω \dd ω = \int_{∂Ω} ω \). Read more
Asymptotic Structure and Symmetries of FLRW Universes · PDF
Honours project supervised by Prof. David Wiltshire at the University of Canterbury. There is a fascinating relationship between the asymptotic symmetries of spacetime and gravitational waves and memory, sometimes referred to as The Infrared Triangle. We investigated the asymptotic structures of simple cosmological spacetimes, extending the usual analysis for flat... Read more
Computing Crystal Band Structures with CP2K · PDF
Summer project about the theory behind numerical computation of the semiconductor band structure of crystals using the open source software CP2K. Full PDF. Read more
Visualising the Freudenreich 1998 Model of the Galactic Bar and Disk · PDF
Cosmology summer project in which we reproduced an empirical model of our galaxy’s centre and wrote code to visualise it. Full PDF. Read more