A thesis submitted March 19, 2015 for the degree of Doctor of Philosophy and defended April 23, 2015.
The PhD School of Science
Faculty of Science
Niels Bohr Institute
University of Copenhagen
Poul Henrik Damgaard
Scattering Amplitudes via Algebraic Geometry Methods
This thesis describes recent progress in the understanding of the mathematical structure of
scattering amplitudes in quantum field theory. The primary purpose is to develop an enhanced analytic framework for computing multiloop scattering amplitudes in generic gauge theories including QCD without Feynman diagrams. The study of multiloop scattering amplitudes is crucial for the new era of precision
phenomenology at the Large Hadron Collider (LHC) at CERN. Loop-level scattering amplitudes can be reduced to a basis of linearly independent integrals whose
coefficients are extracted from generalized unitarity cuts.
We take advantage of principles from algebraic geometry in order to extend the notion of maximal cuts to a large class of two- and three-loop integrals. This allows us to derive unique and surprisingly compact formulae for the coefficients of the basis integrals. Our results are expressed in terms of certain linear combinations of
multivariate residues and elliptic integrals computed from products of tree-level amplitudes. Several explicit examples are provided