A novel infrared regulator for matching lattice to continuum QCD

The success of quantum field theory calculations performed in the perturbative regime provides strong support for the current techniques. The non-perturbative regime, however, requires less straightforward quantitative analyses than its high-energy counterpart. A modern approach to performing non-perturbative QCD calculations is to employ an effective field theory, such as a lattice gauge theory, which is constructed specifically to reproduce the physics of the complete theory. This is achieved by tuning the strength of the effective interactions through a matching procedure: the operators of the effective theory Lagrangian are matched to scattering amplitudes calculated in the perturbative regime of the full theory. M atching calculations require that one employ the same infrared regulator for both the effective and full theory components of the calculation. Unfortunately, some common regulators do not preserve gauge invariance for calculations at orders higher than one loop, and are therefore not generally useful. We are interested in regulators that are suitable for all orders of perturbation theory. Furthermore, matching calculations for the lattice theory are often treated via computer, thereby demanding a regulator that is computer programmable. In this thesis we present the use of twisted boundary conditions as a framework which regulates infrared physics and is suitable for high-order computer based perturbation theory. We also introduce a program for performing calculations with this technology and provide several examples of its use.