| Summary: | Scattering amplitudes are fundamental and remarkably rich observables in quantum field theory. The basic observation that makes scattering amplitudes fascinating is that in theories with massless particles of spin s ≥ 1, they are much simpler than might be expected from traditional Feynman diagram techniques for computing them. This simple observation might ultimately have profound consequences for our view of quantum field theory. The broad aim of this thesis is to understand and exploit the hidden simplicity and structure in scattering amplitudes. The quantum field theory with the simplest scattering amplitudes in four dimensions is planar N = 4 supersymmetric Yang-Mills theory. This theory has provided considerable inspiration in developing new computational techniques and has provided many important theoretical insights. In this theory, there is a remarkable correspondence between scattering amplitudes and null polygonal Wilson loops, observables which on first inspection look very different. In this thesis, we will provide new insights into this correspondence using methods from twistor theory and exploit the symmetries of the problem to find new ways of computing scattering amplitudes.
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