An Introduction to Quantum Field Theory

by Peskin,Michael E.

• ISBN13: 9780201503975
• ISBN10: 0201503972
• Format: Hardcover
• Copyright: 1995-10-02
• Publisher: CRC Press

Summary

An Introduction to Quantum Field Theoryis a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.

Author Biography

Michael E. Peskin received his doctorate in physics from Cornell University and has held research appointments in theoretical physics at Harvard, Cornell, and CEN Saclay. In 1982, he joined the staff of the Stanford Linear Accelerator Center, where he is now Professor of Physics. Daniel V. Schroeder received his doctorate in physics from Stanford University in 1990. He held visiting appointments at Pomona College before joining the faculty of Weber State University, where he is now Associate Professor of Physics. Michael E. Peskin received his doctorate in physics from Cornell University and has held research appointments in theoretical physics at Harvard, Cornell, and CEN Saclay. In 1982, he joined the staff of the Stanford Linear Accelerator Center, where he is now Professor of Physics. Daniel V. Schroeder received his doctorate in physics from Stanford University in 1990. He held visiting appointments at Pomona College before joining the faculty of Weber State University, where he is now Associate Professor of Physics.

Table of Contents

Preface	xi
Notations and Conventions	xix
Editor's Foreword	xxii
Part I: Feynman Diagrams and Quantum Electrodynamics
Invitation: Pair Production in e+e- Annihilation	3	(10)
The Klein-Gordon Field	13	(22)
The Necessity of the Field Viewpoint	13	(2)
Elements of Classical Field Theory	15	(4)
The Klein-Gordon Field as Harmonic Oscillators	19	(6)
The Klein-Gordon Field in Space-Time	25	(10)
Problems	33	(2)
The Dirac Field	35	(42)
Lorentz Invariance in Wave Equations	35	(5)
The Dirace Equation	40	(5)
Free-Particle Solutions of the Dirac Equation	45	(4)
Dirac Matrices and Dirac Field Bilinears	49	(3)
Quantization of the Dirac Field	52	(12)
Discrete Symmetries of the Dirac Theory	64	(13)
Problems	71	(6)
Interacting Fields and Feynman Diagrams	77	(54)
Perturbation Theory---Philosophy and Examples	77	(5)
Perturbation Expansion of Correlation Functions	82	(6)
Wick's Theorem	88	(2)
Feynman Diagrams	90	(9)
Cross Sections and the S-Matrix	99	(9)
Computing S-Matrix Elements from Feynman Diagrams	108	(7)
Feynman Rules for Fermions	115	(8)
Feynman Rules for Quantum Electrodynamics	123	(8)
Problems	126	(5)
Elementary Processes of Quantum Electrodynamics	131	(44)
e+e-→ μ+μ-: Introduction	131	(10)
e+e- → μ+μ-: Helicity Structure	141	(5)
e+e- → μ+μ-: Nonrelativistic Limit	146	(7)
Crossing Symmetry	153	(5)
Compton Scattering	158	(17)
Problems	169	(6)
Radiative Corections: Introduction	175	(36)
Soft Bremsstrahlung	176	(8)
The Electron Vertex Function: Formal Structure	184	(5)
The Electron Vertex Function: Evaluation	189	(10)
The Electron Vertex Function: Infrared Divergence	199	(3)
Summation and Interpretation of Infrared Divergences	202	(9)
Problems	208	(3)
Radiative Corrections: Some Formal Developments	211	(54)
Field-Strength Renormalization	211	(11)
The LSZ Reduction Formula	222	(8)
The Optical Theorem	230	(8)
The Ward-Takahashi Identity	238	(6)
Renormalization of the Electric Charge	244	(21)
Problems	257	(2)
Final Project: Radiation of Gluon Jets	259	(6)
Part II: Renormalization
Invitation: Ultraviolet Cutoffs and Critical Fluctuations	265	(10)
Functional Methods	275	(40)
Path Integrals in Quantum Mechanics	275	(7)
Functional Quantization of Scalar Fields	282	(10)
Quantum Field Theory and Statistical Mechanics	292	(2)
Quantization of the Electromagnetic Field	294	(4)
Functional Quantization of Spinor Fields	298	(8)
Symmetries in the Functional Formalism	306	(9)
Problems	312	(3)
Systematics of Renormalization	315	(32)
Counting of Ultraviolet Divergences	315	(8)
Renormalized Perturbation Theory	323	(7)
Renormalization of Quantum Electrodynamics	330	(5)
Renormalization Beyond the Leading Order	335	(3)
A Two-Loop Example	338	(9)
Problems	344	(3)
Renormalization and Symmetry	347	(46)
Spontaneous Symmetry Breaking	348	(4)
Renormalization and Symmetry: An Explicit Example	352	(12)
The Effective Action	364	(6)
Computation of the Effective Action	370	(9)
The Effective Action as a Generating Functional	379	(4)
Renormalization and Symmetry: General Analysis	383	(10)
Problems	389	(4)
The Renormalization Group	393	(46)
Wilson's Approach to Renormalization Theory	394	(12)
The Callan-Symanzik Equation	406	(12)
Evolution of Coupling Constants	418	(10)
Renormalization of Local Operators	428	(4)
Evolution of Mass Parameters	432	(7)
Problems	438	(1)
Critical Exponents and Scalar Field Theory	439	(34)
Theory of Critical Exponents	440	(11)
Critical Behavior in Four Dimensions	451	(3)
The Nonlinear Sigma Model	454	(19)
Problems	466	(3)
Final Project: The Coleman-Weinberg Potential	469	(4)
Part III: Non-Abelian Gauge Theories
Invitation: The Parton Model of Hadron Structure	473	(8)
Non-Abelian Gauge Invariance	481	(24)
The Geometry of Gauge Invariance	482	(4)
The Yang-Mills Lagrangian	486	(5)
The Gauge-Invariant Wilson Loop	491	(4)
Basic Facts About Lie Algebras	495	(10)
Problems	502	(3)
Quantization of Non-Abelian Gauge Theories	505	(40)
Interactions of Non-Abelian Gauge Bosons	506	(6)
The Faddeev-Popov Lagrangian	512	(3)
Ghosts and Unitarity	515	(2)
BRST Symmetry	517	(4)
One-Loop Divergences of Non-Abelian Gauge Theory	521	(12)
Asymptotic Freedom: The Background Field Method	533	(8)
Asymptotic Freedom: A Qualitative Explanation	541	(4)
Problems	544	(1)
Quantum Chromodynamics	545	(54)
From Quarks to QCD	545	(3)
e+e- Annihilation into Hadrons	548	(7)
Deep Inelastic Scattering	555	(8)
Hard-Scattering Processes in Hadron Collisions	563	(11)
Parton Evolution	574	(19)
Measurements of αs	593	(6)
Problems	595	(4)
Operator Products and Effective Vertices	599	(52)
Renormalization of the Quark Mass Parameter	599	(6)
QCD Renormalization of the Weak Interactions	605	(7)
The Operator Product Expansion	612	(3)
Operator Analysis of e+e- Annihilation	615	(6)
Operator Analysis of Deep Inelastic Scattering	621	(30)
Problems	647	(4)
Perturbation Theory Anomalies	651	(38)
The Axial Current in Two Dimensions	651	(8)
The Axial Current in Four Dimensions	659	(8)
Goldstone Bosons and Chiral Symmetries in QCD	667	(9)
Chiral Anomalies and Chiral Gauge Theories	676	(6)
Anomalous Breaking of Scale Invariance	682	(7)
Problems	686	(3)
Gauge Theories with Spontaneous Symmetry Breaking	689	(42)
The Higgs Mechanism	690	(10)
The Glashow-Weinberg-Salam Theory of Weak Interactions	700	(19)
Symmetries of the Theory of Quarks and Leptons	719	(12)
Problems	728	(3)
Quantization of Spontaneously Broken Gauge Theories	731	(50)
The Rξ Gauges	732	(11)
The Goldstone Boson Equivalence Theorem	743	(15)
One-Loop Corrections in Weak-Interaction Gauge Theory	758	(23)
Problems	773	(2)
Final Project: Decays of the Higgs Boson	775	(6)
Epilogue
Quantum Field Theory at the Frontier	781	(20)
Strong Strong Interactions	782	(4)
Grand Unification and its Paradoxes	786	(5)
Exact Solutions in Quantum Field Theory	791	(4)
Supersymmetry	795	(3)
Toward an Ultimate Theory of Nature	798	(3)
Appendix: Reference Formulae	801	(10)
A.1 Feynman Rules	801	(2)
A.2 Polarizations of External Particles	803	(2)
A.3 Numerator Algebra	805	(1)
A.4 Loop Integrals and Dimensional Regularization	806	(2)
A.5 Cross Sections and Decay Rates	808	(1)
A.6 Physical Constants and Conversion Factors	809	(2)
Bibliography	811	(6)
Index	817