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E-raamat: Foundations Of Quantum Chromodynamics: An Introduction To Perturbative Methods In Gauge Theories (2nd Edition)

(Fukuyama Univ, Japan)
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Foundations Of Quantum Chromodynamics: An Introduction To Perturbative Methods In Gauge Theories (2nd Edition)Suurem pilt
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Discusses in detail the techniques developed for the perturbative regime of Quantum Chromodynamics (QCD) a non-Abelian gauge field theory which successfully describes the strong interactions of fundamental particles. Written to be as self-contained as possible, it starts at a first-year graduate student's level and contains a large amount of background material for QCD, which may also serve as an introduction to gauge field theories. The rest of the book covers the renormalization group method, the operator-product expansion and other technical developments. QCD predictions based on these techniques are derived for short-distance reactions, and the final chapter discusses infrared divergence because of its relevance to the validity argument of the perturbative treatment. Annotation c. by Book News, Inc., Portland, Or.
Preface to the Second Edition vii(2)
Preface to the First Edition xi
Chapter
1. Introduction
1(23)
1.1. General Survey
1(6)
1.2. Quarks and Color
7(8)
1.2.1. Low-lying baryon states
9(1)
1.2.2. Quark confinement
10(1)
1.2.3. Indirect experiemental evidences
11(4)
1.3. Needs for Asymptotic Freedom
15(6)
1.4. Notation and Conventions
21(3)
Chapter
2. Elements of Quantum Chromodynamics
24(156)
2.1. Gauge Priciple
24(11)
2.1.1. Electrodynamics
24(5)
2.1.2. Yang-Mills theories
29(6)
2.2. Quantization
35(22)
2.2.1. Trouble with the canonical quantization
35(4)
2.2.2. Quantization in the Feynman functional-integral formalism
39(8)
2.2.3. Quantization of gauge fields
47(6)
2.2.4. Fermions
53(4)
2.3. Feynman Rules
57(46)
2.3.1. S matrix and Green functions
57(14)
2.3.2. Phi(3) theory
71(10)
2.3.3. Quantum chromodynamics
81(14)
2.3.4. Simple example in e+ e- annihilation
95(3)
2.3.5. Covariant canonical quantization of gauge fields
98(5)
2.4. Regularization
103(21)
2.4.1. Review of regularization schemes
103(6)
2.4.2. Dimensional regularization
109(1)
2.4.3. Preliminary remarks on renormalization schemes
119(5)
2.5. Renormalization
124(56)
2.5.1. Power counting
124(4)
2.5.2. Renormalizable interactions
128(4)
2.5.3. Renormalization in phi(3) theory
132(17)
2.5.4. BPHZ method in phi(3) theory
149(8)
2.5.5. Quantum chromodynamics
157(16)
2.5.6. Generalized Ward-Takahashi identities
173(7)
Chapter
3. Renormalization Group Method
180(42)
3.1. Renormalization Group
180(6)
3.1.1. Finite renormalization
180(3)
3.1.2. Group of finite renormalizations
183(3)
3.2. Renormalization group equations
186(13)
3.2.1. Renormalization group equation in the MS scheme
186(6)
3.2.2. The renormalization group equation in other schemes
192(7)
3.3. Soultion of the Renormalization Group Equations
199(7)
3.3.1. Soultion of the 't Hooft-Weinberg equation
199(2)
3.3.2. Behavior of the solution
201(5)
3.4. Asymptotic Freedom
206(11)
3.4.1. Renormalization group functions in QCD
206(8)
3.4.2. Asymptotic freedom in QCD
214(2)
3.4.3. Renormalization group functions in other theories
216(1)
3.5. Anomalous Dimensions
217(5)
Chapter
4. Operator Product Expansion
222(46)
4.1. Operator Products
222(12)
4.1.1. Composite operators
222(3)
4.1.2. Product of currents in deep inelastic scatterings
225(6)
4.1.3. Product of currents in e+ e- annihilations
231(3)
4.2. Operator-product Expansion in Perturbation Theory
234(29)
4.2.1. Free field theory
234(4)
4.2.2. The parton model
238(5)
4.2.3. Renormalization of composite operators
243(6)
4.2.4. Proof of the operator product expansion
249(13)
4.2.5. Light-cone expansion
262(1)
4.3. Coefficient Functions
263(5)
4.3.1. Singularity in coefficient functions
263(1)
4.3.2. Renormalization group equations
264(4)
Chapter 5 Physical Applications
268(63)
5.1. Total Cross Section for e+ e- Annihilations
268(10)
5.1.1. Renormalization group equation
268(2)
5.1.2. Order-g(2) correction
270(7)
5.1.3. Higher-order corrections
277(1)
5.2. Deep Inelastic Lepton-hadron Scatterings
278(29)
5.2.1. Moment sum rules for structure functions
278(5)
5.2.2. Renormalization-group-improved perturbation
283(6)
5.2.3. Flavor structure of composite operators
289(2)
5.2.4. The nonsinglet part
291(6)
5.2.5. The single part
297(3)
5.2.6. Experimental tests
300(7)
5.3. Renormalization-scheme Dependence
307(8)
5.3.1. Renormalization-scheme dependence of perturbative predictions
307(4)
5.3.2. Beta function and anomalous dimensions
311(1)
5.3.3. e+ e- annihilations and deep inelastic scatterings
312(3)
5.4. Jets
315(7)
5.4.1. qq jets in e+ e- annihilations
315(5)
5.4.2. Higher order effects
320(1)
5.4.3. Experimental observation
321(1)
5.5. Factorization and the Drell-Yan Process
322(9)
Chapter
6. Infrared Divergences
331(40)
6.1. One-loop Example
331(14)
6.1.1. Origin of infrared divergences
331(3)
6.1.2. Regularization
334(4)
6.1.3. Cancellation of infrared divergences
338(7)
6.2. Proof of the Soft-photon Cancellation in QED
345(10)
6.2.1. Soft-photon emission
345(6)
6.2.2. Virtual photons
351(3)
6.2.3. Cancellation
354(1)
6.3. General Arguments for Infrared Cancellation
355(16)
6.3.1. Infrared divergence in QCD
355(3)
6.3.2. The Kinoshita-Poggio-Quinn theorem
358(6)
6.3.3. The Kinoshita-Lee-Nauenberg theorem
364(7)
Appendix A: One-loop Contribution to Superficially Divergent Feynman Amplitudes in QCD 371(9)
Appendix B: Useful Formulas involving the SU(N) Generators 380(2)
Appendix C: Renormalization Constants in QCD 382(2)
Appendix D: Feynman Rules 384(1)
Bibliography 384(19)
Index 403


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