THE SCHWINGER-DYSON EQUATIONS AND GLUON BOUND STATES OF QCD
Nonperturbative techniques in quantum field theory have been successful in describing both the propagator functions and bound states of various theories, most notably those of quarks and hadrons in Quantum Chromodynamics (QCD). The nonperturbative theoretical framework is presented from basic principles and developed, through examples in a variety of quantum field theories, as a general numerical approach which can yield valuable insight into quantum phenomenology. Explorations include the studies which I have performed to extend this description to the gauge sector of QCD, including the influence of both gluon and ghost fields. This allows for the description of gluon bound states (“Glueballs”) which are theoretically viable explanations for previously unidentified resonances in experimental particle searches. This description is sufficiently robust to provide commentary on the valence gluon content of conventional meson bound states. Additionally, the premier investigation of the full two-loop gluon gap equation is presented and discussed, along with general commentary on the current state of nonpeturbative QCD.