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作者 Gogokhia, Vakhtang
書名 Mass Gap And Its Applications, The
出版項 Singapore : World Scientific Publishing Company, 2013
©2013
國際標準書號 9789814440714 (electronic bk.)
9789814440707
book jacket
說明 1 online resource (252 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
附註 Intro -- 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
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 mass-spectrum of QCD, one needs the mass scale parameter (the mass gap) instead of other massive particles. The energy difference between the lowest order and the vacuum state in Yang-Mills quantum field theory, the mass gap is in principle responsible for the large-scale structure of the QCD ground state, and thus also for its non-perturbative phenomena at low energies. This book not only presents the mass gap, but also details the applications and outlook of the mass gap method. A detailed summary of references and problems are included as well.This book is best for scientists and highly advanced students interested in non-perturbative effects and methods in QCD
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Gogokhia, Vakhtang Mass Gap And Its Applications, The Singapore : World Scientific Publishing Company,c2013 9789814440707
主題 Yang-Mills theory.;Quantum chromodynamics
Electronic books
Alt Author Barnafoldi, Gergely Gabor
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