Scattering Amplitudes in Genus 3

Abstract

The first part of this thesis is a short introduction to scattering amplitudes, aimed at algebraic geometers with not very much physics background. We try to emphasize simple examples and give a rough survey of topics: Feynman diagrams, tree and loop level, on-shell diagrams, the spinor-helicity formalism, BCFW recursion, the Parke-Taylor formula, and maximum helicity violating amplitudes. Next, we explain Tevelev’s attempt to apply this circle of ideas to curves. We try to give new examples and flesh out detail that is left implicit in his original paper. We work out a few amplitude forms in genus 2 and 3 and graph their probability densities. We end by discussing some possible directions for new work.