The Schwinger-Dyson Equations and Gluon Bound States of QCD

[摘要] Nonperturbative techniques in quantum field theory, such as lattice gauge theory, Schwinger- Dyson equations, and applications of the renormalization group, 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 Schwinger-Dyson 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 bound state theory 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, and is treated for the first time using the Bethe-Salpeter formalism. This description is sufficiently robust to explore the spectrum of glueballs and provide commentary on the potential for investigation of valence gluon content in meson bound states. Additionally, the first investigation of the full two-loop gluon gap equation is presented and discussed, along with general commentary on the current state of nonperturbative QCD. This computation yields the dressed propagators for quarks, gluons, and ghosts from the coupled set of equations.

[发布机构] the University of Pittsburgh