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Quantum Chromodynamics (QCD) is the most up-to-date theory of the strong interaction. Its predictions have been verified experimentally, and it is a cornerstone of the Standard Model of particle physics. However, standard perturbative procedures fail if applied to low-energy QCD. Even the discovery of the Higgs Boson will not solve the problem of masses originating from the non-perturbative behavior of QCD.This book presents a new method, the introduction of the 'mass gap', first suggested by Arthur Jaffe and Edward Witten at the turn of the millennium. It attempts to show that, to explain the

Yang-Mills theory. --- Quantum chromodynamics. --- Chromodynamics, Quantum --- QCD (Nuclear physics) --- Particles (Nuclear physics) --- Quantum electrodynamics --- Mills-Yang theory --- Yang-Mills theories --- Quantum field theory

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The author develops a novel analysis method for QCD sum rules (QCDSR) by applying the maximum entropy method (MEM) to arrive at an analysis with less artificial assumptions than previously held. This is a first-time accomplishment in the field. In this thesis, a reformed MEM for QCDSR is formalized and is applied to the sum rules of several channels: the light-quark meson in the vector channel, the light-quark baryon channel with spin and isospin 1/2, and several quarkonium channels at both zero and finite temperatures. This novel technique of combining QCDSR with MEM is applied to the study of quarkonium in hot matter, which is an important probe of the quark-gluon plasma currently being created in heavy-ion collision experiments at RHIC and LHC.

Bayesian statistical decision theory. --- Gauge fields (Physics) -- Mathematics. --- Quantum chromodynamics -- Mathematics. --- Quantum chromodynamics --- Bayesian statistical decision theory --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Mathematics --- Mathematics. --- Bayes' solution --- Bayesian analysis --- Chromodynamics, Quantum --- QCD (Nuclear physics) --- Physics. --- Mathematical physics. --- Quantum field theory. --- String theory. --- Elementary particles (Physics). --- Quantum Field Theories, String Theory. --- Elementary Particles, Quantum Field Theory. --- Mathematical Physics. --- Statistical decision --- Particles (Nuclear physics) --- Quantum electrodynamics --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Physical mathematics --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Models, String --- String theory --- Nuclear reactions --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics)

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Gaining a theoretical understanding of the properties of ultra-relativistic dense matter has been one of the most important and challenging goals in quantum chromodynamics (QCD). In this thesis, the author analyzes dense quark matter in QCD with gauge group SU(2) using low-energy effective theoretical techniques and elucidates a novel connection between statistical properties of the Dirac operator spectrum at high baryon chemical potential and a special class of random matrix theories. This work can be viewed as an extension of a similar correspondence  between QCD and matrix models which was previously known only for infinitesimal chemical potentials. In future numerical simulations of dense matter the analytical results reported here are expected to serve as a useful tool to extract physical observables such as the BCS gap from numerical data on the Dirac spectrum.

Relativistic fluid dynamics. --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Nuclear Physics --- Dirac equation. --- Quantum chromodynamics. --- Chromodynamics, Quantum --- QCD (Nuclear physics) --- Physics. --- Energy. --- Mathematical physics. --- Quantum field theory. --- String theory. --- Elementary particles (Physics). --- Quantum Field Theories, String Theory. --- Elementary Particles, Quantum Field Theory. --- Mathematical Physics. --- Energy, general. --- Particles (Nuclear physics) --- Quantum electrodynamics --- Differential equations, Partial --- Quantum field theory --- Wave equation --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Physical mathematics --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Models, String --- String theory --- Nuclear reactions --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Mathematics