AbstractsPhysics

Scattering amplitudes provide a handle for testing and constraining quantum field theories. In this thesis, I explore two directions within the topic: 1) using amplitudes to probe how the number of degrees of freedom evolves as the energy scale changes along renormalization group flows, and 2) extending a new modern approach to computing amplitudes that reveals the intriguing underlying mathematical structure. In the first part, I generalize a method that encodes the flow of degrees of freedom into certain scattering amplitudes from four dimensions to arbitrary dimensions and uncover new structures that become relevant in eight dimensions. I also demonstrate that scattering of other massless modes cannot interfere with the 4d method. In the second part, I explore a reformulation of tree-level amplitudes in 4d N=4 super Yang-Mills (SYM) theory in terms of a contour integral over the space of k x n matrices and show how to extend several aspects beyond N=4 SYM theory. A key new result is an algorithm I developed to resolve an important sign ambiguity in calculating residues of the contour integral. Advisors/Committee Members: Elvang, Henriette Dina-Maria (committee member), Lam, Thomas (committee member), Larsen, Finn (committee member), Liu, James T (committee member), Amidei, Dante Eric (committee member).