Lectures on Quantum Chromodynamics Book

	Preface
	Notation and Conventions
	Introduction: Some History
Pt. 1	Foundations
Lecture 1	Yang-Mills Field	3
1.1	Path Ordered Exponentials, Invariant Actions	3
1.2	Classical Solutions	11
Lecture 2	Instantons	15
2.1	Topological Charge	15
2.2	Explicit Solutions	19
Lecture 3	Path Integral in Quantum Mechanics	25
3.1	Conventional Approach	25
3.2	Euclidean Path Integral	30
3.3	Holomorphic Representation	32
3.4	Grassmann Dynamic Variables	34
Lecture 4	Quantization of Gauge Theories	39
4.1	Dirac Quantization Procedure	39
4.2	Path Integral on the Lattice	49
Lecture 5	[theta]-Vacuum	55
5.1	Quantum Pendulum	55
5.2	Large Gauge Transformations in Non-Abelian Theory	62
Pt. 2	Perturbation Theory
Lecture 6	Diagram Technique in Simple and Complicated Theories	69
6.1	Feynman Rules from Path Integral	70
6.2	Fixing the Gauge	76
Lecture 7	When the Gauge is Fixed ...	85
7.1	Gribov Copies	85
7.2	Ward Identities	88
7.3	Ghosts and Unitarity	92
7.4	BRST Quantization	96
Lecture 8	Regularization and Renormalization	103
8.1	Different Regularization Schemes	103
8.2	Renormalized Theory as an Effective Theory. Slavnov-Taylor Identities	109
Lecture 9	Running Coupling Constant	119
9.1	One-loop Calculations	119
9.2	Renormalization Group. Asymptotic Freedom and Infrared Slavery	127
9.3	Observables. Ambituities. Anomalous Dimensions	133
Lecture 10	Weathering Infrared Storms	143
10.1	Bloch-Nordsieck Cancellation	144
10.2	Non-Abelian Complications. Coherent States	151
Lecture 11	Collinear Singularities: Theory and Phenomenology	157
11.1	Double Logarithmic Asymptotics	157
11.2	Jet Cross Sections	159
11.3	DIS and KLN	165
Pt. 3	Nonperturbative QCD
Lecture 12	Symmetries: Anomalous and Not	177
12.1	Conformal Symmetry and its Breaking	179
12.2	Anomalous Chiral Symmetry	184
12.3	Nonsinglet Chiral Symmetry and its Spontaneous Breaking	193
12.4	Effective Chiral Langrangian	196
Lecture 13	Quarks on Euclidean Lattice	199
13.1	Nielsen-Ninomiya's No-go Theorem	199
13.2	Ways to Go. The Ginsparg - Wilson Way	203
Lecture 14	Aspects of Chiral Symmetry	211
14.1	QCD Inequalities. Vafa - Witten Theorem	211
14.2	Euclidean Dirac Spectral Density	214
14.3	Infrared Face of Anomaly	219
14.4	Chiral Symmetry Breaking and Confinement	223
Lecture 15	Mesoscopic QCD	227
15.1	Partition Function: N[subscript f] = 1	227
15.2	Partition Function: N[subscript f] [is greater than or equal to] 2	230
15.3	Spectral Sum Rules	232
15.4	Instanton Gas and Instanton Liquid	234
Lecture 16	Fairy QCD	241
16.1	Finite [theta]	241
16.2	Large N[subscript c]	247
Lecture 17	ITEP Sum Rules: the Duality Festival	255
17.1	The Method	255
17.2	Nucleon Mass and Residue	257
17.3	Pion Formfactor and Nucleon Magnetic Moments	268
Lecture 18	Hot and Dense QCD	275
18.1	Lukewarm Pion Gas. Restoration of Chiral Symmetry	277
18.2	Quark-Gluon Plasma	282
18.3	Finite Baryon Density. Color Superconductivity	287
Lecture 19	Confinement	291
19.1	Weak Confinement and Strong Confinement. Wilson Criterium	292
19.2	Schwinger Model	295
19.3	Polyakov Model	298
19.4	Dual Superconductivity	302
App	Unitary groups	307
	Bibliography	315
	Index	319