The Mass Gap and Its Applications

The following sections are included:

• Dedication

• Preface

• Acknowledgments

• Contents

The following sections are included:

• Quantum Chromodynamics

• The Jaffe – Witten theorem on the Mass Gap

• Problems

The following sections are included:

• Introduction

• The gluon Schwinger – Dyson equation

• Transversality of the full gluon self-energy

• Slavnov – Taylor identity for the full gluon propagator

• The general structure of the full gluon propagator

• Non-perturbative vs. Perturbative QCD

• The Mass Gap

• Subtraction at the fundamental gluon propagator level

• Discussion

• Appendix: Application for Abelian case

• Problems

The following sections are included:

• Introduction

• Singular solution

• Massive solution

• Conclusions

• Appendix: The dimensional regularization method in the perturbation theory

• Appendix: The dimensional regularization method in the distribution theory

• Problems

The following sections are included:

• Introduction

• The intrinsically non-perturbative gluon propagator

• Confining gluon propagator

• The renormalized running effective charge

• The general criterion of gluon confinement

• The general criterion of quark confinement

• The general criterion of dynamical/spontaneous breakdown of chiral symmetry

• Physical limits

• Asymptotic freedom and the mass gap

• Appendix: The Weierstrass – Sokhatsky – Casorati theorem

• Problems

The following sections are included:

• Discussion

• Subtractions

• Conclusions

The following sections are included:

• Introduction

• The vacuum energy density

• The intrinsically non-perturbative vacuum energy density

• The bag constant

• Analytical and numerical evaluation of the bag constant

• The trace anomaly relation

• Comparison with phenomenology

• Numerical values for B_YM in different units

• Contribution of B_YM to the dark energy problem

• Energy from the QCD vacuum

• Conclusions

• Appendix: The general role of ghosts

• Problems

The following sections are included:

• Introduction

• The gluon pressure at zero temperature

• The gluon pressure at non-zero temperature

• The scale-setting scheme

• The P_NP(T) contribution

• Conclusions

• Appendix: The summation of the thermal logarithms

• Problems

The following sections are included:

• Introduction

• Analytic thermal perturbation theory

• Convergence of the perturbation theory series

• The gluon pressure, P_g(T)

• Low-temperature expansion

• High-temperature expansion

• Discussion and conclusions

• Problems

The following sections are included:

• Introduction

• The gluon pressure P_g(T)

• The full gluon plasma pressure

• Main thermodynamic quantities

• The Stefan – Boltzmann limit

• Analytical formulae for the gluon plasma thermodynamic quantities

• Double-counting in integer powers of α_s problem

• Numerical results and discussion

• The dynamical structure of SU(3) gluon plasma

• Conclusions

• Appendix: Analytical and numerical evaluation of the latent heat

• Appendix: The β-function for the confining effective charge at non-zero temperature

• Appendix: Least Mean Squares method and the definition of the average deviation

• Appendix: Restoration of the lattice pressure below 0.9T_c

• Problems

The following sections are included:

• Bibliography

• Index