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a SlavnovTaylor Identities
a Renormalization Group Equation
a Vacuum Polarization Equation
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approach arbitrary asymptotic freedom asymptotic infrared region axial gauge Bar-Gadda Boson Bound State Equation bound-state color confinement constraint construct derivation dimensional DOCTOR OF PHILOSOPHY dynamical effective coupling effective equation extended structure four gluon gauge invariant gauge transformation ghost self-energy gluon terms gluon vacuum polarization hadronic Hooft infrared behavior infrared divergent infrared effective infrared singular integrals kinematical singularities ladder approximation Lagrangian Landau gauge Lett mass momentum non-Abelian gauge theory non-perturbative Nucl observe obtain one-particle irreducible order parameter perturbation Phys physical mechanisms polarization tensor preprint QCD vacuum quadruple gluon Quantum Chromodynamics quantum field theory quark propagator quark self-energy read this thesis remaining terms renormaliz renormalization constants renormalization group equation satisfied Schwinger-Dyson equations scope and quality self-consistency condition Slavnov Slavnov-Taylor identity Equation space-time straightforward to show Substituting superconductivity t'Hooft terms figs topological expansion transverse triple gluon vertex vacuum polarization equation vacuum polarization term vanishes Ward identities wavefunction Zachariasen zero