Research
Published:
Research Summary
I am interested in applying analytical and differential geometric techniques to solve problems in classical and quantum physics. Previous work has covered areas in:
- classical electrodynamics (linear, nonlinear, scattering)
- quantum electrodynamics (Casimir stresses, light-matter interaction)
- continuum mechanics (elasticity, fluid dynamics)
- General Relativity (gravitational waves, astrophysical jets, cosmology)
My published work has application to areas such as star formation; laser-plasma acceleration; quantum encryption; the genesis of astrophysical jets; and modelling the early Universe.
Tools of the Trade
Exterior differential geometry is the natural mathematical language to discuss differential properties of tensor fields on spacetime and their relation to integrals over material domains. My work heavily exploits this calculus to elucidate problems in relativistic spacetime physics. There are numerous references for differential geometry and General Relativity, but the one that has had the most impact is:
- An Introduction to Spinors and Geometry with Applications in Physics
Ian M. Benn and Robin W. Tucker;
Adam Hilger Ltd, Bristol (1987)
The main reason for this is that one of the authors (Robin W. Tucker) was my PhD supervisor; hence this book contains the majority of notation and conventions that permeate my own work. I would point to the following resource:
- A Primer on Exterior Differential Calculus
David A. Burton
Theoretical and Applied Mechanics, 30 (2003), 85-162
which delivers an excellent pedagogical introduction to differential forms and their application in physics.
My Academic Network
My collaborators include:
- Robin W. Tucker (Lancaster University, UK)
- David A. Burton (Lancaster University, UK)
- Adam Noble (University of Strathclyde, UK)
- Shinichiro Goto (Chubu University, Japan)
- Manuel Arrayás (Universidad Rey Juan Carlos, Spain)
- José Luis Trueba (Universidad Rey Juan Carlos, Spain)
For a bit of fun, here is some information about my academic network:
- my academic genealogy
- Erdős number: 4
- Einstein number: 5 (as calculated by MathSciNet)