Amplitude Calculations Using Algebraic Geometry
In a recent paper (ArXiv 1205.5707) Yang Zhang, a post-doc at the Discovery Center, has demonstrated a method to calculate multi-loop corrections to scattering amplitudes, using tools from the mathematical discipline of Algebraic Geometry.
A commonly used method to find loop-level amplitudes, known as Generalized Unitarity, consist of expressing the amplitude in terms of a basis of known integrals. Hitherto no systematic way of finding such a basis has been known in general for two or more loops, but Yang succeeded in re-expressing the problem in terms of Algebraic Geometry, and using results from there to construct a computer program able to find such a basis independently of the number of loops. Further work on finding loop-order amplitudes is progress by Yang and collaborators at the Discovery Center.