QCD near the light front

In this thesis, we propose a set of techniques to study the non-perturbative behavior of quantum field theories. These techniques include the use of near light front coordinates and a theory of effective Hamiltonians;Our ultimate goal will be to apply these methods to quantum electrodynamics (QED) and quantum chromodynamics (QCD). As a first test we will investigate simplified versions of QED and QCD with these methods over all ranges or their coupling constants;First, we solve the Schwinger model, which is QED in one space and one time dimension. We use this test model in both the massless and massive fermion cases to show the efficacy of our coordinate choice, as well as to resolve certain technical issues arising from our choice of coordinate system. New analytic results are obtained for the massive case;Second, starting from the QCD Lagrangian, we present the SU(2) QCD Hamiltonian written in near-light front coordinates. We investigate the dynamics of the gluonic zero modes of this Hamiltonian, and obtain explicit strong and weak coupling solutions. We also calculate the energies of a few low-lying states in the two-site cluster approximation, utilizing effective Hamiltonian theory for the full range of coupling strength. The existence of confinement is already evident at this level of approximation;Our present applications do not require renormalization. However, for more realistic future studies, we introduce a way of implementing renormalization within the context of the theory of effective Hamiltonians. Our renormalization scheme is independent of any specific kinematics. We show how to calculate the beta function within this context and exhibit our method using simple scale-invariant quantum mechanical systems