Quantum Chromodynamics

by Greiner, Walter; Schramm, Stefan; Stein, Eckart

• ISBN13: 9783540666103
• ISBN10: 3540666109
• Edition: 2nd
• Format: Paperback
• Copyright: 2002-10-01
• Publisher: Springer Verlag

Summary

The book is a self-contained introduction to perturbative and nonperturbative quantum Chromodynamics (QCD) with worked-out exercises for students of theoretical physics. It will be useful as a reference for research scientists as well. Starting with the hadron spectrum, the reader becomes familiar with the representations of SU(N). Relativistic quantum field theory is recapitulated, and scattering theory is discussed in the framework of scalar quantum electrodynamics. Then the gauge theory of quarks and gluons is introduced. In the more advanced chapters, perturbative and nonperturbative techniques in state-of-the-art QCD are discussed in great detail. This completely revised and enlarged second edition will fill the gap in the literature.

Table of Contents

The Introduction of Quarks	1	(16)
The Hadron Spectrum	1	(16)
Review of Relativistic Field Theory	17	(58)
Spinor Quantum Electrodynamics	17	(8)
The Free Dirac Equation and Its Solution	17	(3)
Density and Current Density	20	(1)
Covariant Notation	21	(1)
Normalization of Dirac Spinors	21	(2)
Interaction with a Four-Potential Aμ	23	(1)
Transition Amplitudes	24	(1)
Discrete Symmetries	24	(1)
Scalar Quantum Electrodynamics	25	(31)
The Free Klein-Gordon Equation and Its Solutions	25	(3)
Interaction of a π+ with a Potential Aμ	28	(3)
π+K+ Scattering	31	(3)
The Cross Section	34	(11)
Spin-1 Particles and Their Polarization	45	(6)
The Propagator for Virtual Photons	51	(5)
Fermion-Boson and Fermion-Fermion Scattering	56	(19)
Traces and Spin Summations	58	(10)
The Structure of the Form Factors from Invariance Considerations	68	(7)
Scattering Reactions and the Internal Structure of Baryons	75	(78)
Simple Quark Models Compared	75	(3)
The Description of Scattering Reactions	78	(45)
The MIT Bag Model	123	(30)
Gauge Theories and Quantum-Chromodynamics	153	(84)
The Standard Model: A Typical Gauge Theory	153	(10)
The Gauge Theory of Quark-Quark Interactions	163	(19)
Dimensional Regularization	182	(18)
The Renormalized Coupling Constant of QCD	200	(17)
Extended Example: Anomalies in Gauge Theories	217	(20)
The Schwinger Model on the Circle	217	(2)
Dirac Sea	219	(2)
Ultraviolet Regularization	221	(4)
Standard Derivation	225	(2)
Anomalies in QCD	227	(1)
The Axial and Scale Anomalies	228	(6)
Mulitloop Corrections	234	(3)
Perturbative QCD 1: Deep Inelastic Scattering	237	(148)
The Gribov-Lipatov-Altarelli-Parisi Equations	237	(26)
An Alternative Approach to the Glap Equations	263	(16)
Common Parametrizations of the Distribution Functions and Anomalous Dimensions	279	(11)
Renormalization and the Expansion Into Local Operators	290	(36)
Calculation of the Wilson Coefficients	326	(28)
The Spin-Dependent Structure Functions	354	(31)
Perturbative QCD II: The Drell-Yan Process and Small-x Physics	385	(54)
The Drell-Yan Process	385	(43)
Small-x Physics	428	(11)
Nonperturbative QCD	439	(74)
Lattice QCD Calculations	440	(48)
The Path Integral Method	440	(5)
Expectation Values	445	(2)
Qcd on the Lattice	447	(2)
Gluons on the Lattice	449	(3)
Integration in SU(2)	452	(2)
Discretization: Scalar and Fermionic Fields	454	(5)
Fermionic Path Intergral	459	(2)
Monte Carlo Methods	461	(2)
Metropolis Algorithm	463	(1)
Langevin Algorithms	464	(2)
The Microcanonical Algorithms	466	(6)
Strong and Weak Coupling Expansions	472	(2)
Weak-Coupling Approximation	474	(1)
Larger Loops in the Limit of Weak and Strong Coupling	475	(2)
The String Tension	477	(3)
The Lattice at Finite Temperature	480	(3)
The Quark Condensate	483	(2)
The Polyakov Loop	485	(1)
The Center Symmetry	486	(2)
QCD Sum Rules	488	(25)
Phenomenological Models for Nonperturbative QCD Problems	513	(26)
The Ground State of QCD	513	(15)
The Quark-Gluon Plasma	528	(11)
Appendix	539	(8)
A The Group SU (N)	539	(2)
B Dirac Algebra in Dimension d	541	(3)
C Some Useful Integrals	544	(3)
Subject Index	547