Applications and Developments in the Effective Field Theory Approach to Forward Scattering in Gauge Theories and Gravity

In this thesis, we study the forward limit in gauge theories and gravity using the tools of Soft Collinear Effective Theory (SCET) with Glauber operators. For gauge theories, we derive relations for the anomalous dimensions of hard scattering operators in terms of diagrams with Glauber gluon exchanges from unitarity and analyticity considerations. Similar arguments can be applied to the forward scattering amplitude and Glauber operators, leading to new relations, constraints, and calculation techniques for these operators. We then generalize the Glauber SCET approach to the problem of gravitational scattering, and we use this to study classical gravitational scattering. We find an infinite tower of large logarithms in the classical phase, and we describe how they may be calculated at any desired order in perturbation theory.