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E-raamat: Qcd Vacuum, Hadrons And Superdense Matter, The (2nd Edition)

(State Univ Of New York At Stony Brook, Usa)
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This invaluable book is an extensive set of lecture notes on various aspects of non-perturbative quantum chromodynamics the fundamental theory of strong interaction on which nuclear and hadronic physics is based.The original edition of the book, written in the mid-1980's, had more of a review style. In the second edition the outline remains the same, but the text has been completely rewritten, and extended. Apart from the new developments over the years, this edition has benefited from several graduate courses which the author has taught at Stony Brook during the last decade. The text is now complemented by exercises and has a total of about 1000 references to major works, arranged by subject.Three major issues the structure of the QCD vacuum, the structure of hadrons, and the physics of hot/dense matter are addressed as physics problems. Therefore, when discussing any specific subject, the book attempts to incorporate (1) all the solid theoretical results, (2) experimental information, and (3) results of numerical (lattice) simulations, which are playing an increasing role in quantum field theory in general, and the development of QCD in particular.The QCD Vacuum, Hadrons and Superdense Matter takes the reader from the first encounter with the subject to the front line of research, as quickly as possible.
Preface xv
Chapter 1 Theoretical Introduction 1(50)
1.1. Gauge Fields
2(10)
1.1.1. Gauge "symmetry"
2(2)
1.1.2. Gauge fields on the lattice
4(3)
1.1.3. Fixing the gauge
7(1)
1.1.4. Hamiltonian quantization
8(1)
1.1.5. Rotator - a toy model for periodic coordinates
9(3)
1.2. Road to QCD
12(4)
1.2.1. Quarks and the "colors"
12(1)
1.2.2. Renormalizability and asymptotic freedom
12(4)
1.3. Path Integrals and Euclidean Time
16(8)
1.3.1. Green functions and Feynman path integrals
16(4)
1.3.2. Perturbation theory and Euclidean path integrals
20(3)
1.3.3. Numerical evaluation of Euclidean path integrals
23(1)
1.4. Guage Fields on the Lattice
24(8)
1.4.1. Renormalization group and asymptotic freedom
26(2)
1.4.2. Continuum limit of lattice gauge theory
28(2)
1.4.3. Path integrals for fermions
30(2)
1.5. Light Quarks and Symmetries of QCD
32(10)
1.5.1. Exact and approximate symmetries of QCD
32(2)
1.5.2. Chiral anomalies, the UV approach
34(4)
1.5.3. Chiral anomalies, the IR approach
38(1)
1.5.4. Other applications of chiral anomalies
39(1)
1.5.5. Scale Anomaly
40(2)
1.6. Heavy Quarks, New Symmetry and Effective Theory
42(3)
1.7. Changing the Number of Colors Nc
45(6)
1.7.1. Large number of colors
45(4)
1.7.2. QCD with the smallest (Nc = 2) number of colors
49(2)
Chapter 2 Phenomenology of the QCD Vacuum 51(54)
2.1. Phenomenology of the Hadronic World
52(12)
2.1.1. Brief history
52(3)
2.1.2. The "usual" hadrons
55(1)
2.1.3. The "unusual" mesons
56(3)
2.1.4. The exotic hadrons
59(2)
2.1.5. Remarks about highly excited states
61(3)
2.2. Models of Hadronic Structure
64(13)
2.2.1. Generalities
64(2)
2.2.2. MIT bag
66(2)
2.2.3. Skyrmions
68(2)
2.2.4. Chiral bags
70(1)
2.2.5. Evolving views on the nature of the spin forces
71(6)
2.3. Models of the QCD Vacuum: An Overview
77(6)
2.3.1. Condensates and scales
77(1)
2.3.2. Condensate factorization and stochastic vacuum model
78(2)
2.3.3. An example of a highly inhomogeneous model: the instanton vacuum
80(3)
2.4. Chiral Symmetry Breaking and Effective Low Energy Theory
83(12)
2.4.1. Spontaneous breaking of the chiral symmetry
83(1)
2.4.2. The Goldstone modes: oscillations of the quark condensate
84(2)
2.4.3. Quark condensate and Dirac eigenvalue spectrum
86(2)
2.4.4. Elements of chiral perturbation theory
88(2)
2.4.5. Effective chiral Lagrangian
90(3)
2.4.6. Nambu-Jona-Lasinio model
93(2)
2.5. Color Confinement
95(10)
2.5.1. Static potential
95(2)
2.5.2. Dual superconductivity
97(1)
2.5.3. Structure of flux tubes
98(3)
2.5.4. Interaction of flux tubes
101(4)
Chapter 3 Euclidean Theory of Tunneling: From Quantum Mechanics to Gauge Theories 105(36)
3.1. Tunneling in Quantum Mechanics
105(10)
3.1.1. Brief history of tunneling
105(1)
3.1.2. Double-well problem and instantons
106(3)
3.1.3. Pre-exponent and zero modes
109(2)
3.1.4. Instanton gas
111(2)
3.1.5. Two-loop quantum corrections
113(2)
3.2. A Digression: Tunneling Versus Perturbative Series
115(6)
3.2.1. Convergence of perturbative series
115(3)
3.2.1.1. Dyson instability
115(1)
3.2.1.2. Perturbative series in high orders
116(1)
3.2.1.3. Semiclassical evaluation of Dyson's instability
117(1)
3.2.1.4. High orders of perturbative series in field theories
118(1)
3.2.2. Instanton-anti-instanton interaction and one more correction to the ground state energy
118(3)
3.3. Fermions Coupled to the Double-Well Potential
121(3)
3.4. Instantons in Gauge Theories
124(8)
3.4.1. Topologically nontrivial objects
124(1)
3.4.2. Topologically distinct pure gauge configurations
125(2)
3.4.3. Digression: spherically symmetric Yang-Mills fields
127(1)
3.4.4. Static magnetic configurations and their minimal energy
128(4)
3.5. Tunneling and BPST Instanton
132(9)
3.5.1. Instanton solution
132(4)
3.5.2. Theta vacua
136(2)
3.5.3. Tunneling amplitude
138(3)
Chapter 4 Instanton Ensemble in QCD 141(52)
4.1. Brief History of Instantons
141(5)
4.1.1. Discovery and early applications
141(1)
4.1.2. Phenomenology leads to a qualitative picture
142(1)
4.1.3. Technical development during 1980's
143(1)
4.1.4. Recent progress
144(1)
4.1.5. Instantons at finite temperatures and chiral restoration
145(1)
4.1.6. Instantons and color superconductivity at high densities
145(1)
4.2. Tunneling and Light Quarks
146(6)
4.2.1. Relating gauge field topology to the axial charge
146(1)
4.2.2. Fermionic zero modes
147(2)
4.2.3. The 't Hooft effective interaction
149(2)
4.2.4. Baryon number violation in the standard model
151(1)
4.3 Instanton Ensemble
152(18)
4.3.1. Qualitative discussion of the instanton ensembles
152(4)
4.3.2. Mean field approximation: pure glue
156(3)
4.3.3. Quark condensate in the mean field approximation
159(6)
4.3.4. The single instanton approximation
165(5)
4.4. The Interacting Instanton Liquid Model
170(10)
4.4.1 Screening of the topological charge
178(2)
4.5. Instantons for Larger Number of Colors
180(13)
4.5.1. Naive counting and expectations
181(1)
4.5.2. Mean field arguments and the chiral condensate
182(2)
4.5.3. Fluctuations in the interacting instanton liquid
184(2)
4.5.4. Do instantons cluster at large Nc?
186(7)
Chapter 5 Lattice QCD 193(34)
5.1. Generalities
193(11)
5.1.1. Brief history
193(2)
5.1.2. Lattice limitations
195(3)
5.1.3. Mesoscopic regime and the random matrix theory
198(3)
5.1.4. Art of numerical simulation of multi-dimensional integrals
201(3)
5.2. Fermions on the lattice
204(4)
5.2.1. Fermionic doublers
204(1)
5.2.2. Wilson fermions
205(1)
5.2.3. Ginsparg-Wilson relation and lattice chiral symmetry
206(1)
5.2.4. Known solutions to GW relation
206(1)
5.2.5. Domain wall fermions
207(1)
5.3. Hadronic spectroscopy on the lattice
208(6)
5.3.1. Glueballs in gluodynamics
209(1)
5.3.2. Light quark spectroscopy in quenched approximation
210(2)
5.3.3. Spectroscopy with dynamical quarks
212(2)
5.4. Topology on the lattice
214(13)
5.4.1. Quantum-mechanical topology and perfect actions
214(4)
5.4.2. Naive and geometric methods for gauge fields
218(3)
5.4.3. Are the lowest Dirac eigenstates locally chiral?
221(4)
5.4.4. Testing the large Nc limit on the lattice
225(2)
Chapter 6 QCD Correlation Functions 227(74)
6.1. Generalities
227(9)
6.1.1. Why the correlation functions?
227(3)
6.1.2. Different representations of the correlation functions
230(2)
6.1.3. Quantum numbers and inequalities
232(2)
6.1.4. Correlators with chirality flips
234(2)
6.2. Phenomenology of Mesonic Correlation Functions
236(16)
6.2.1. Vector and axial correlators
236(8)
6.2.2. Comparing axial and vector channels
244(2)
6.2.3. Pseudoscalar SU(3) octet (π, Kappa, η) channels
246(2)
6.2.4. SU(3) singlet pseudoscalars
248(2)
6.2.5. Hadron-parton duality
250(2)
6.3. Operator Product Expansion and QCD Sum Rules
252(18)
6.3.1. Brief history and overview
252(2)
6.3.2. Separation of scales
254(1)
6.3.3. OPE in a background field
255(5)
6.3.4. Sum rules for heavy-light mesons
260(2)
6.3.5. OPE for light quark baryons
262(3)
6.3.6. OPE for mesons made of light quarks
265(5)
6.4. Instantons and the Correlators: Analytic Results
270(9)
6.4.1. Propagator in the field of a single instanton
270(1)
6.4.2. First order in the 't Hooft effective vertex
271(2)
6.4.3. Propagator in the instanton ensemble
273(2)
6.4.4. Propagator in the mean field approximation
275(1)
6.4.5. Correlators in the random phase approximation
276(3)
6.5. Correlators in the Instanton Liquid
279(14)
6.5.1. Quark propagator in the instanton liquid
279(1)
6.5.2. Mesonic correlators
280(4)
6.5.3. Baryonic correlation functions
284(3)
6.5.4. Comparison to correlators on the lattice
287(1)
6.5.5. Gluonic correlation functions
288(5)
6.6. Hadronic Structure and n-Point Correlators
293(8)
6.6.1. Wave functions
294(1)
6.6.2. Form factors
295(6)
Chapter 7 High Energy Hadronic Collisions 301(36)
7.1. Introduction
301(9)
7.1.1. Reggions and the Pomeron
301(2)
7.1.2. High energy collisions in pQCD and its "phases"
303(4)
7.1.3. Evolving descriptions of soft Pomeron dynamics
307(3)
7.2. Instanton-Induced Processes at High Energies
310(20)
7.2.1. Toward the "holy grail"
310(1)
7.2.2. Exciting a quantum system from under the barrier
311(1)
7.2.3. Semiclassical production of sphaleron-like clusters
312(2)
7.2.4. Explosion of the turning states
314(2)
7.2.5. Semiclassical evaluation of the cross section
316(1)
7.2.6. Semiclassical Wilson lines
317(6)
7.2.7. Pomeron from instantons
323(7)
7.3. Pomeron Structure and Interactions
330(7)
7.3.1. Clustering in inclusive pp collisions
330(1)
7.3.2. Inclusive production of clusters in double-Pomeron processes
331(3)
7.3.3. Exclusive production of hadrons in double-Pomeron processes
334(3)
Chapter 8 QCD at Finite Temperatures 337(66)
8.1. Introduction
337(13)
8.1.1. Brief history and the basic scales
337(2)
8.1.2. From field theory to thermodynamics
339(1)
8.1.3. A quantum particle at finite T
340(6)
8.1.4. Gauge and fermion fields at finite T
346(4)
8.2. QCD at High Temperatures
350(13)
8.2.1. Screening versus anti-screening
350(3)
8.2.2. Thermodynamical potential in the lowest order
353(1)
8.2.3. Ring diagram re-summation
354(2)
8.2.4. IR divergences in general
356(1)
8.2.5. Are perturbative series useful in practice?
357(2)
8.2.6. HTL re-summations and the quasiparticle gas
359(3)
8.2.7. Viscosity of the QGP
362(1)
8.3. Hadronic Matter
363(5)
8.3.1. Pion gas at low T
363(1)
8.3.2. Resonance gas
364(2)
8.3.3. Pion liquid
366(2)
8.4. QCD Phase Transitions at Finite T
368(13)
8.4.1. Deconfinement
368(3)
8.4.2. Chiral symmetry restoration
371(3)
8.4.3. Static quark potential at high T
374(2)
8.4.4. Equation of state in the transition region
376(5)
8.5. Instantons at Finite T
381(13)
8.5.1. Finite temperature field theory and the caloron solution
381(1)
8.5.2. Instanton density at high temperature
382(4)
8.5.3. Instantons at low temperature
386(1)
8.5.4. Chiral symmetry restoration and instantons
387(2)
8.5.5. Instanton ensemble in the phase transition region
389(3)
8.5.6. Critical behavior in the instanton liquid
392(2)
8.6. Hadronic Correlation Functions at Finite Temperature
394(9)
8.6.1. Screening masses
395(2)
8.6.2. Temporal correlation functions
397(2)
8.6.3. U(1)A breaking at high T
399(4)
Chapter 9 Excited Hadronic Matter in Heavy Ion Collisions 403(74)
9.1. Introduction
403(7)
9.1.1. Toward the macroscopic limit
403(3)
9.1.2. "Little Bang" versus Big Bang
406(2)
9.1.3. Experimental centers, present and future
408(1)
9.1.4. Mapping the phase diagram
409(1)
9.2. Relativistic Hydrodynamics
410(11)
9.2.1. Equations of the ideal hydrodynamics
410(3)
9.2.2. Dissipative terms
413(1)
9.2.3. The Bjorken solution
414(2)
9.2.4. Further simplifications and solutions
416(1)
9.2.5. Singularities: shocks, rarefaction waves, and the "explosive edge"
417(4)
9.3. Chemical and Thermal Freezeouts
421(15)
9.3.1. Why two freezeouts?
421(2)
9.3.2. Chemical freezeout
423(1)
9.3.3. Between chemical and kinetic freezeouts
423(5)
9.3.4. Thermal freezeout
428(3)
9.3.5. After freezeout
431(1)
9.3.6. Freezeout of resonances and nuclear fragments
432(1)
9.3.7. Resonance modification
433(3)
9.4. Hydrodynamic Description of Heavy Ion Data
436(23)
9.4.1. A long road to unveiling the transverse flow
436(4)
9.4.2. Qualitative effects of the QCD phase transition
440(2)
9.4.3. Solutions to hydrodynamic equations
442(3)
9.4.4. Radial flow at SPS and RHIC
445(4)
9.4.5. Elliptic flow
449(6)
9.4.6. Limits to ideal hydrodynamics
455(4)
9.5. Interferometry of Identical Secondaries or HBT Method
459(7)
9.5.1. Main idea of the method
459(2)
9.5.2. Correlator and random source model
461(2)
9.5.3. Issue of "coherency" and long-lived resonances
463(1)
9.5.4. Expanding sources and regions of homogeneity
464(2)
9.6. Correlation of Non-Identical Hadrons
466(3)
9.6.1. Ordering the production time for all hadronic species
467(1)
9.6.2. Balance functions
467(2)
9.7. Event-by-Event Fluctuations
469(8)
9.7.1. Fluctuations of hadronic cross sections are surprisingly large
469(1)
9.7.2. All heavy ion collisions are (about) the same!
470(2)
9.7.3. Critical opalescence near the tricritical point
472(3)
9.7.4. Can QGP charge fluctuations survive the hadronic phase?
475(2)
Chapter 10 Early Diagnostics of Hadronic Matter 477(42)
10.1. Penetrating Probes: Dileptons and Photons
477(11)
10.1.1. Basic rates and space-time profile
477(3)
10.1
2. Dilepton data versus expectations
480(6)
10.1.3. Direct photon production
486(2)
10.2. Quarkonia in Heavy Ion Collisions
488(4)
10.2.1. Charmonium suppression, the mechanisms
488(1)
10.2.2. Charmonium suppression, the data
489(2)
10.2.3. φ-related puzzles
491(1)
10.3. Evolving Views on the Initial Stage
492(5)
10.3.1. Perturbative processes and minijets
492(1)
10.3.2. Classical fields in heavy ion collisions
493(2)
10.3.3. Non-perturbative equilibration and topological clusters
495(1)
10.3.4. Dilemma of weakly versus strongly coupled QGP
496(1)
10.4. Jet Quenching
497(22)
10.4.1. Jet quenching in experiment
498(5)
10.4.2. Azimuthal asymmetry at large pt
503(2)
10.4.3. Radiation in matter
505(2)
10.4.4. Synchrotron-like QCD radiation
507(12)
Chapter 11 QCD at High Density 519(34)
11.1. From Nuclear to Quark Matter
519(12)
11.1.1. Nuclear matter
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)
11.2. Compact Stars
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)
11.3.10. Open questions
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)
A.2: Units
575(1)
A.3: Space-Time and Other Indices, Standard Matrices
576(1)
A.4: Properties of η Symbols
576(1)
A.5: Gauge Fields
577(1)
A.6: Quark Fields
578(1)
A.7: QCD Feynman Rules
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)
B.3: Group Integration
583(2)
Appendix C A Sample Program for Numerical Simulation of the Euclidean Quantum Paths 585(2)
Bibliography 587(30)
Index 617