Research
Canonical Group Quantization
Currently, I’m working on Canonical Group Quantization, a quantization method for non-trivial phase spaces originally developed by Christopher Isham. The general idea is that group actions of a classical theory can be used to obtain a so-called Canonical Group. The associated quantum theory is then given by representations of this group. An advantage of Canonical Group Quantization over other quantization methods is that it remains relatively transparent from a physical point of view and that it doesn’t axiomatize away the problems.
If you want to learn more about this interesting quantization approach you should have a look at the talk on Canonical Group Quantization I’ve given at the Theorie-Palaver in 2010, or at my latest poster.
Geometric Algebra
During my diploma thesis I was interested in Geometric Algebra. Geometric Algebra, based on Clifford algebra, unifies different mathematical formalisms in a unique, geometrical way and thereby brings fresh insights into known physical problems. One example is the Kepler problem, which can be rewritten as a simple harmonic oszillator using so called rotors. Besides this, Pauli and Dirac spin matrices get a deep geometrical meaning and pop up everywhere, even when not talking about spin.
You can read more about Geometric Algebra in the introductionary paper Imaginary Numbers are not Real written at the Cavendish Laboratory in Cambridge. Another good starting point is David Hestenes’ Oersted Medal Lecture: Reforming the Mathematical Language of Physics. If you can understand german you might also be interested in my diploma thesis.
