Preface |
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xv | |
Chapter 1 Theoretical Introduction |
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1 | (50) |
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2 | (10) |
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2 | (2) |
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1.1.2. Gauge fields on the lattice |
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4 | (3) |
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7 | (1) |
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1.1.4. Hamiltonian quantization |
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8 | (1) |
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1.1.5. Rotator - a toy model for periodic coordinates |
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9 | (3) |
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12 | (4) |
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1.2.1. Quarks and the "colors" |
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12 | (1) |
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1.2.2. Renormalizability and asymptotic freedom |
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12 | (4) |
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1.3. Path Integrals and Euclidean Time |
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16 | (8) |
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1.3.1. Green functions and Feynman path integrals |
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16 | (4) |
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1.3.2. Perturbation theory and Euclidean path integrals |
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20 | (3) |
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1.3.3. Numerical evaluation of Euclidean path integrals |
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23 | (1) |
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1.4. Guage Fields on the Lattice |
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24 | (8) |
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1.4.1. Renormalization group and asymptotic freedom |
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26 | (2) |
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1.4.2. Continuum limit of lattice gauge theory |
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28 | (2) |
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1.4.3. Path integrals for fermions |
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30 | (2) |
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1.5. Light Quarks and Symmetries of QCD |
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32 | (10) |
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1.5.1. Exact and approximate symmetries of QCD |
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32 | (2) |
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1.5.2. Chiral anomalies, the UV approach |
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34 | (4) |
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1.5.3. Chiral anomalies, the IR approach |
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38 | (1) |
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1.5.4. Other applications of chiral anomalies |
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39 | (1) |
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40 | (2) |
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1.6. Heavy Quarks, New Symmetry and Effective Theory |
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42 | (3) |
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1.7. Changing the Number of Colors Nc |
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45 | (6) |
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1.7.1. Large number of colors |
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45 | (4) |
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1.7.2. QCD with the smallest (Nc = 2) number of colors |
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49 | (2) |
Chapter 2 Phenomenology of the QCD Vacuum |
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51 | (54) |
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2.1. Phenomenology of the Hadronic World |
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52 | (12) |
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52 | (3) |
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2.1.2. The "usual" hadrons |
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55 | (1) |
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2.1.3. The "unusual" mesons |
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56 | (3) |
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2.1.4. The exotic hadrons |
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59 | (2) |
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2.1.5. Remarks about highly excited states |
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61 | (3) |
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2.2. Models of Hadronic Structure |
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64 | (13) |
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64 | (2) |
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66 | (2) |
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68 | (2) |
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70 | (1) |
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2.2.5. Evolving views on the nature of the spin forces |
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71 | (6) |
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2.3. Models of the QCD Vacuum: An Overview |
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77 | (6) |
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2.3.1. Condensates and scales |
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77 | (1) |
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2.3.2. Condensate factorization and stochastic vacuum model |
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78 | (2) |
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2.3.3. An example of a highly inhomogeneous model: the instanton vacuum |
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80 | (3) |
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2.4. Chiral Symmetry Breaking and Effective Low Energy Theory |
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83 | (12) |
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2.4.1. Spontaneous breaking of the chiral symmetry |
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83 | (1) |
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2.4.2. The Goldstone modes: oscillations of the quark condensate |
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84 | (2) |
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2.4.3. Quark condensate and Dirac eigenvalue spectrum |
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86 | (2) |
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2.4.4. Elements of chiral perturbation theory |
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88 | (2) |
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2.4.5. Effective chiral Lagrangian |
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90 | (3) |
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2.4.6. Nambu-Jona-Lasinio model |
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93 | (2) |
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95 | (10) |
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95 | (2) |
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2.5.2. Dual superconductivity |
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97 | (1) |
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2.5.3. Structure of flux tubes |
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98 | (3) |
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2.5.4. Interaction of flux tubes |
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101 | (4) |
Chapter 3 Euclidean Theory of Tunneling: From Quantum Mechanics to Gauge Theories |
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105 | (36) |
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3.1. Tunneling in Quantum Mechanics |
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105 | (10) |
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3.1.1. Brief history of tunneling |
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105 | (1) |
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3.1.2. Double-well problem and instantons |
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106 | (3) |
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3.1.3. Pre-exponent and zero modes |
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109 | (2) |
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111 | (2) |
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3.1.5. Two-loop quantum corrections |
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113 | (2) |
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3.2. A Digression: Tunneling Versus Perturbative Series |
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115 | (6) |
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3.2.1. Convergence of perturbative series |
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115 | (3) |
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3.2.1.1. Dyson instability |
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115 | (1) |
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3.2.1.2. Perturbative series in high orders |
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116 | (1) |
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3.2.1.3. Semiclassical evaluation of Dyson's instability |
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117 | (1) |
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3.2.1.4. High orders of perturbative series in field theories |
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118 | (1) |
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3.2.2. Instanton-anti-instanton interaction and one more correction to the ground state energy |
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118 | (3) |
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3.3. Fermions Coupled to the Double-Well Potential |
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121 | (3) |
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3.4. Instantons in Gauge Theories |
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124 | (8) |
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3.4.1. Topologically nontrivial objects |
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124 | (1) |
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3.4.2. Topologically distinct pure gauge configurations |
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125 | (2) |
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3.4.3. Digression: spherically symmetric Yang-Mills fields |
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127 | (1) |
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3.4.4. Static magnetic configurations and their minimal energy |
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128 | (4) |
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3.5. Tunneling and BPST Instanton |
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132 | (9) |
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3.5.1. Instanton solution |
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132 | (4) |
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136 | (2) |
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3.5.3. Tunneling amplitude |
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138 | (3) |
Chapter 4 Instanton Ensemble in QCD |
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141 | (52) |
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4.1. Brief History of Instantons |
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141 | (5) |
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4.1.1. Discovery and early applications |
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141 | (1) |
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4.1.2. Phenomenology leads to a qualitative picture |
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142 | (1) |
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4.1.3. Technical development during 1980's |
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143 | (1) |
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144 | (1) |
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4.1.5. Instantons at finite temperatures and chiral restoration |
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145 | (1) |
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4.1.6. Instantons and color superconductivity at high densities |
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145 | (1) |
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4.2. Tunneling and Light Quarks |
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146 | (6) |
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4.2.1. Relating gauge field topology to the axial charge |
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146 | (1) |
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4.2.2. Fermionic zero modes |
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147 | (2) |
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4.2.3. The 't Hooft effective interaction |
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149 | (2) |
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4.2.4. Baryon number violation in the standard model |
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151 | (1) |
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152 | (18) |
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4.3.1. Qualitative discussion of the instanton ensembles |
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152 | (4) |
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4.3.2. Mean field approximation: pure glue |
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156 | (3) |
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4.3.3. Quark condensate in the mean field approximation |
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159 | (6) |
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4.3.4. The single instanton approximation |
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165 | (5) |
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4.4. The Interacting Instanton Liquid Model |
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170 | (10) |
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4.4.1 Screening of the topological charge |
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178 | (2) |
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4.5. Instantons for Larger Number of Colors |
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180 | (13) |
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4.5.1. Naive counting and expectations |
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181 | (1) |
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4.5.2. Mean field arguments and the chiral condensate |
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182 | (2) |
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4.5.3. Fluctuations in the interacting instanton liquid |
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184 | (2) |
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4.5.4. Do instantons cluster at large Nc? |
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186 | (7) |
Chapter 5 Lattice QCD |
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193 | (34) |
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193 | (11) |
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193 | (2) |
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5.1.2. Lattice limitations |
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195 | (3) |
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5.1.3. Mesoscopic regime and the random matrix theory |
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198 | (3) |
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5.1.4. Art of numerical simulation of multi-dimensional integrals |
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201 | (3) |
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5.2. Fermions on the lattice |
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204 | (4) |
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5.2.1. Fermionic doublers |
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204 | (1) |
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205 | (1) |
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5.2.3. Ginsparg-Wilson relation and lattice chiral symmetry |
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206 | (1) |
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5.2.4. Known solutions to GW relation |
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206 | (1) |
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5.2.5. Domain wall fermions |
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207 | (1) |
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5.3. Hadronic spectroscopy on the lattice |
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208 | (6) |
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5.3.1. Glueballs in gluodynamics |
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209 | (1) |
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5.3.2. Light quark spectroscopy in quenched approximation |
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210 | (2) |
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5.3.3. Spectroscopy with dynamical quarks |
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212 | (2) |
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5.4. Topology on the lattice |
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214 | (13) |
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5.4.1. Quantum-mechanical topology and perfect actions |
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214 | (4) |
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5.4.2. Naive and geometric methods for gauge fields |
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218 | (3) |
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5.4.3. Are the lowest Dirac eigenstates locally chiral? |
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221 | (4) |
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5.4.4. Testing the large Nc limit on the lattice |
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225 | (2) |
Chapter 6 QCD Correlation Functions |
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227 | (74) |
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227 | (9) |
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6.1.1. Why the correlation functions? |
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227 | (3) |
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6.1.2. Different representations of the correlation functions |
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230 | (2) |
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6.1.3. Quantum numbers and inequalities |
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232 | (2) |
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6.1.4. Correlators with chirality flips |
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234 | (2) |
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6.2. Phenomenology of Mesonic Correlation Functions |
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236 | (16) |
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6.2.1. Vector and axial correlators |
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236 | (8) |
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6.2.2. Comparing axial and vector channels |
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244 | (2) |
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6.2.3. Pseudoscalar SU(3) octet (π, Kappa, η) channels |
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246 | (2) |
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6.2.4. SU(3) singlet pseudoscalars |
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248 | (2) |
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6.2.5. Hadron-parton duality |
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250 | (2) |
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6.3. Operator Product Expansion and QCD Sum Rules |
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252 | (18) |
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6.3.1. Brief history and overview |
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252 | (2) |
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6.3.2. Separation of scales |
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254 | (1) |
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6.3.3. OPE in a background field |
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255 | (5) |
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6.3.4. Sum rules for heavy-light mesons |
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260 | (2) |
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6.3.5. OPE for light quark baryons |
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262 | (3) |
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6.3.6. OPE for mesons made of light quarks |
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265 | (5) |
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6.4. Instantons and the Correlators: Analytic Results |
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270 | (9) |
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6.4.1. Propagator in the field of a single instanton |
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270 | (1) |
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6.4.2. First order in the 't Hooft effective vertex |
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271 | (2) |
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6.4.3. Propagator in the instanton ensemble |
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273 | (2) |
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6.4.4. Propagator in the mean field approximation |
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275 | (1) |
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6.4.5. Correlators in the random phase approximation |
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276 | (3) |
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6.5. Correlators in the Instanton Liquid |
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279 | (14) |
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6.5.1. Quark propagator in the instanton liquid |
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279 | (1) |
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6.5.2. Mesonic correlators |
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280 | (4) |
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6.5.3. Baryonic correlation functions |
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284 | (3) |
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6.5.4. Comparison to correlators on the lattice |
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287 | (1) |
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6.5.5. Gluonic correlation functions |
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288 | (5) |
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6.6. Hadronic Structure and n-Point Correlators |
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293 | (8) |
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294 | (1) |
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295 | (6) |
Chapter 7 High Energy Hadronic Collisions |
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301 | (36) |
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301 | (9) |
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7.1.1. Reggions and the Pomeron |
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301 | (2) |
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7.1.2. High energy collisions in pQCD and its "phases" |
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303 | (4) |
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7.1.3. Evolving descriptions of soft Pomeron dynamics |
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307 | (3) |
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7.2. Instanton-Induced Processes at High Energies |
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310 | (20) |
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7.2.1. Toward the "holy grail" |
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310 | (1) |
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7.2.2. Exciting a quantum system from under the barrier |
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311 | (1) |
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7.2.3. Semiclassical production of sphaleron-like clusters |
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312 | (2) |
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7.2.4. Explosion of the turning states |
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314 | (2) |
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7.2.5. Semiclassical evaluation of the cross section |
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316 | (1) |
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7.2.6. Semiclassical Wilson lines |
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317 | (6) |
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7.2.7. Pomeron from instantons |
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323 | (7) |
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7.3. Pomeron Structure and Interactions |
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330 | (7) |
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7.3.1. Clustering in inclusive pp collisions |
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330 | (1) |
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7.3.2. Inclusive production of clusters in double-Pomeron processes |
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331 | (3) |
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7.3.3. Exclusive production of hadrons in double-Pomeron processes |
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334 | (3) |
Chapter 8 QCD at Finite Temperatures |
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337 | (66) |
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337 | (13) |
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8.1.1. Brief history and the basic scales |
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337 | (2) |
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8.1.2. From field theory to thermodynamics |
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339 | (1) |
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8.1.3. A quantum particle at finite T |
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340 | (6) |
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8.1.4. Gauge and fermion fields at finite T |
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346 | (4) |
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8.2. QCD at High Temperatures |
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350 | (13) |
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8.2.1. Screening versus anti-screening |
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350 | (3) |
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8.2.2. Thermodynamical potential in the lowest order |
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353 | (1) |
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8.2.3. Ring diagram re-summation |
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354 | (2) |
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8.2.4. IR divergences in general |
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356 | (1) |
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8.2.5. Are perturbative series useful in practice? |
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357 | (2) |
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8.2.6. HTL re-summations and the quasiparticle gas |
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359 | (3) |
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8.2.7. Viscosity of the QGP |
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362 | (1) |
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363 | (5) |
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363 | (1) |
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364 | (2) |
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366 | (2) |
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8.4. QCD Phase Transitions at Finite T |
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368 | (13) |
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368 | (3) |
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8.4.2. Chiral symmetry restoration |
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371 | (3) |
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8.4.3. Static quark potential at high T |
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374 | (2) |
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8.4.4. Equation of state in the transition region |
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376 | (5) |
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8.5. Instantons at Finite T |
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381 | (13) |
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8.5.1. Finite temperature field theory and the caloron solution |
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381 | (1) |
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8.5.2. Instanton density at high temperature |
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382 | (4) |
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8.5.3. Instantons at low temperature |
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386 | (1) |
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8.5.4. Chiral symmetry restoration and instantons |
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387 | (2) |
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8.5.5. Instanton ensemble in the phase transition region |
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389 | (3) |
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8.5.6. Critical behavior in the instanton liquid |
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392 | (2) |
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8.6. Hadronic Correlation Functions at Finite Temperature |
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394 | (9) |
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395 | (2) |
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8.6.2. Temporal correlation functions |
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397 | (2) |
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8.6.3. U(1)A breaking at high T |
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399 | (4) |
Chapter 9 Excited Hadronic Matter in Heavy Ion Collisions |
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403 | (74) |
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403 | (7) |
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9.1.1. Toward the macroscopic limit |
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403 | (3) |
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9.1.2. "Little Bang" versus Big Bang |
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406 | (2) |
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9.1.3. Experimental centers, present and future |
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408 | (1) |
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9.1.4. Mapping the phase diagram |
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409 | (1) |
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9.2. Relativistic Hydrodynamics |
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410 | (11) |
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9.2.1. Equations of the ideal hydrodynamics |
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410 | (3) |
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413 | (1) |
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9.2.3. The Bjorken solution |
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414 | (2) |
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9.2.4. Further simplifications and solutions |
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416 | (1) |
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9.2.5. Singularities: shocks, rarefaction waves, and the "explosive edge" |
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417 | (4) |
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9.3. Chemical and Thermal Freezeouts |
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421 | (15) |
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9.3.1. Why two freezeouts? |
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421 | (2) |
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9.3.2. Chemical freezeout |
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423 | (1) |
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9.3.3. Between chemical and kinetic freezeouts |
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423 | (5) |
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428 | (3) |
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431 | (1) |
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9.3.6. Freezeout of resonances and nuclear fragments |
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432 | (1) |
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9.3.7. Resonance modification |
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433 | (3) |
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9.4. Hydrodynamic Description of Heavy Ion Data |
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436 | (23) |
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9.4.1. A long road to unveiling the transverse flow |
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436 | (4) |
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9.4.2. Qualitative effects of the QCD phase transition |
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440 | (2) |
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9.4.3. Solutions to hydrodynamic equations |
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442 | (3) |
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9.4.4. Radial flow at SPS and RHIC |
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445 | (4) |
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449 | (6) |
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9.4.6. Limits to ideal hydrodynamics |
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455 | (4) |
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9.5. Interferometry of Identical Secondaries or HBT Method |
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459 | (7) |
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9.5.1. Main idea of the method |
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459 | (2) |
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9.5.2. Correlator and random source model |
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461 | (2) |
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9.5.3. Issue of "coherency" and long-lived resonances |
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463 | (1) |
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9.5.4. Expanding sources and regions of homogeneity |
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464 | (2) |
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9.6. Correlation of Non-Identical Hadrons |
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466 | (3) |
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9.6.1. Ordering the production time for all hadronic species |
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467 | (1) |
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467 | (2) |
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9.7. Event-by-Event Fluctuations |
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469 | (8) |
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9.7.1. Fluctuations of hadronic cross sections are surprisingly large |
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469 | (1) |
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9.7.2. All heavy ion collisions are (about) the same! |
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470 | (2) |
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9.7.3. Critical opalescence near the tricritical point |
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472 | (3) |
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9.7.4. Can QGP charge fluctuations survive the hadronic phase? |
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475 | (2) |
Chapter 10 Early Diagnostics of Hadronic Matter |
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477 | (42) |
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10.1. Penetrating Probes: Dileptons and Photons |
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477 | (11) |
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10.1.1. Basic rates and space-time profile |
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477 | (3) |
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10.1 2. Dilepton data versus expectations |
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480 | (6) |
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10.1.3. Direct photon production |
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486 | (2) |
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10.2. Quarkonia in Heavy Ion Collisions |
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488 | (4) |
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10.2.1. Charmonium suppression, the mechanisms |
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488 | (1) |
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10.2.2. Charmonium suppression, the data |
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489 | (2) |
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10.2.3. φ-related puzzles |
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491 | (1) |
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10.3. Evolving Views on the Initial Stage |
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492 | (5) |
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10.3.1. Perturbative processes and minijets |
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492 | (1) |
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10.3.2. Classical fields in heavy ion collisions |
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493 | (2) |
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10.3.3. Non-perturbative equilibration and topological clusters |
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495 | (1) |
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10.3.4. Dilemma of weakly versus strongly coupled QGP |
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496 | (1) |
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497 | (22) |
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10.4.1. Jet quenching in experiment |
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498 | (5) |
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10.4.2. Azimuthal asymmetry at large pt |
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503 | (2) |
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10.4.3. Radiation in matter |
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505 | (2) |
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10.4.4. Synchrotron-like QCD radiation |
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507 | (12) |
Chapter 11 QCD at High Density |
|
519 | (34) |
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11.1. From Nuclear to Quark Matter |
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519 | (12) |
|
|
519 | (4) |
|
11.1.2. Other phases of nuclear matter? |
|
|
523 | (1) |
|
11.1.3. From nuclear to quark matter |
|
|
523 | (3) |
|
11.1.4. Chiral waves and chiral crystals |
|
|
526 | (5) |
|
|
531 | (5) |
|
11.2.1. Brief introduction |
|
|
531 | (3) |
|
11.2.2. Phases of matter in compact stars |
|
|
534 | (2) |
|
11.3. Color Superconductivity in Very Dense Quark Matter |
|
|
536 | (17) |
|
11.3.1. Brief introduction to superconductivity |
|
|
536 | (3) |
|
11.3.2. BCS pairing and Gorkov abnormal Green functions |
|
|
539 | (1) |
|
11.3.3. Three mechanisms of quark pairing |
|
|
540 | (2) |
|
11.3.4. Magnetic pairing in asymptotically dense matter |
|
|
542 | (3) |
|
11.3.5. Instanton-induced color superconductivity |
|
|
545 | (1) |
|
11.3.6. Two-flavor QCD: 2SC phase |
|
|
546 | (1) |
|
11.3.7. Three-flavor QCD: CFL phase |
|
|
546 | (2) |
|
11.3.8. Excitations of color superconductor |
|
|
548 | (2) |
|
11.3.9. Quark matter with charge neutrality and realistic ms |
|
|
550 | (1) |
|
|
550 | (3) |
Chapter 12 A Wider Picture |
|
553 | (22) |
|
12.1. Hadronic World in Alternative or Changing Universe |
|
|
553 | (2) |
|
12.2. Increasing the Number of Quark Flavors: The First Window to Conformal World |
|
|
555 | (2) |
|
12.3. N = 1 Supersymmetric Theories |
|
|
557 | (8) |
|
12.3.1. Instantons and exact beta function |
|
|
559 | (3) |
|
12.3.2. Nc-Nf phase diagram: N = 1 SUSY versus QCD |
|
|
562 | (3) |
|
12.4. N = 2 Supersymmetric Theories |
|
|
565 | (5) |
|
12.5. N = 4 Supersynunetric Theories and AdS/CFT Correspondence |
|
|
570 | (5) |
|
12.5.1. Conformal field theory |
|
|
570 | (1) |
|
12.5.2. A window to the string world: strong coupling |
|
|
571 | (3) |
|
12.5.3. AdS/CFT duality at weak coupling and instantons |
|
|
574 | (1) |
Appendix A Notations |
|
575 | (6) |
|
A.1: Some Abbreviations Used |
|
|
575 | (1) |
|
|
575 | (1) |
|
A.3: Space-Time and Other Indices, Standard Matrices |
|
|
576 | (1) |
|
A.4: Properties of η Symbols |
|
|
576 | (1) |
|
|
577 | (1) |
|
|
578 | (1) |
|
|
579 | (2) |
Appendix B Basic Instanton Formulae |
|
581 | (4) |
|
B.1: Instanton Gauge Potential |
|
|
581 | (1) |
|
B.2: Fermion Zero Modes and Overlap Integrals |
|
|
582 | (1) |
|
|
583 | (2) |
Appendix C A Sample Program for Numerical Simulation of the Euclidean Quantum Paths |
|
585 | (2) |
Bibliography |
|
587 | (30) |
Index |
|
617 | |