Contents -- Preface -- Acknowledgments -- Theory of the Mass Gap -- 1. Quantum Chromodynamics and the Mass Gap -- 1.1 Quantum Chromodynamics -- 1.2 The Jaffe -Witten theorem on the Mass Gap -- Problems -- 2. Color Gauge Invariance and the Origin of the Mass Gap -- 2.1 Introduction -- 2.2 The gluon Schwinger -Dyson equation -- 2.3 Transversality of the full gluon self-energy -- 2.4 Slavnov -Taylor identity for the full gluon propagator -- 2.5 The general structure of the full gluon propagator -- 2.6 Non-perturbative vs. Perturbative QCD -- 2.7 The Mass Gap -- 2.8 Subtraction at the fundamental gluon propagator level -- 2.9 Discussion -- 2.A Appendix: Application for Abelian case -- Problems -- 3. Formal Exact Solutions for the Full Gluon Propagator at Non-zero Mass Gap -- 3.1 Introduction -- 3.2 Singular solution -- 3.3 Massive solution -- 3.4 Conclusions -- 3.A Appendix: The dimensional regularization method in the perturbation theory -- 3.B Appendix: The dimensional regularization method in the distribution theory -- Problems -- 4. Renormalization of the Mass Gap -- 4.1 Introduction -- 4.2 The intrinsically non-perturbative gluon propagator -- 4.3 Confining gluon propagator -- 4.4 The renormalized running effective charge -- 4.5 The general criterion of gluon confinement -- 4.6 The general criterion of quark confinement -- 4.7 The general criterion of dynamical/spontaneous breakdown of chiral symmetry -- 4.8 Physical limits -- 4.9 Asymptotic freedom and the mass gap -- 4.A Appendix: The Weierstrass - Sokhatsky -Casorati theorem -- Problems -- 5. General Discussion -- 5.1 Discussion -- 5.2 Subtractions -- 5.3 Conclusions -- Applications of the Mass Gap -- 6. Vacuum Energy Density in the Quantum Yang -Mills Theory -- 6.1 Introduction -- 6.2 The vacuum energy density -- 6.3 The intrinsically non-perturbative vacuum energy density.

6.4 The bag constant -- 6.5 Analytical and numerical evaluation of the bag constant -- 6.6 The trace anomaly relation -- 6.7 Comparison with phenomenology -- 6.8 Numerical values for BYM in different units -- 6.9 Contribution of BYM to the dark energy problem -- 6.10 Energy from the QCD vacuum -- 6.11 Conclusions -- 6.A Appendix: The general role of ghosts -- Problems -- 7. The Non-perturbative Analytical Equation of State for the Gluon Matter I -- 7.1 Introduction -- 7.2 The gluon pressure at zero temperature -- 7.3 The gluon pressure at non-zero temperature -- 7.4 The scale-setting scheme -- 7.5 The PNP (T ) contribution -- 7.6 Conclusions -- 7.A Appendix: The summation of the thermal logarithms -- Problems -- 8. The Non-perturbative Analytical Equation of State for the Gluon Matter II -- 8.1 Introduction -- 8.2 Analytic thermal perturbation theory -- 8.3 Convergence of the perturbation theory series -- 8.4 The gluon pressure, Pg(T ) -- 8.5 Low-temperature expansion -- 8.6 High-temperature expansion -- 8.7 Discussion and conclusions -- Problems -- 9. The Non-perturbative Analytical Equation of State for SU(3) Gluon Plasma -- 9.1 Introduction -- 9.2 The gluon pressure Pg(T ) -- 9.3 The full gluon plasma pressure -- 9.4 Main thermodynamic quantities -- 9.5 The Stefan -Boltzmann limit -- 9.6 Analytical formulae for the gluon plasma thermodynamic quantities -- 9.7 Double-counting in integer powers of s problem -- 9.8 Numerical results and discussion -- 9.9 The dynamical structure of SU(3) gluon plasma -- 9.10 Conclusions -- 9.A Appendix: Analytical and numerical evaluation of the latent heat -- 9.B Appendix: The -function for the confining effective charge at non-zero temperature -- 9.C Appendix: Least Mean Squares method and the definition of the average deviation -- 9.D Appendix: Restoration of the lattice pressure below 0.9Tc -- Problems.

Bibliography -- Index.