An Introduction to Quantum Field Theory

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Cambridge University Press, Aug 26, 1993 - Science - 572 pages
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This is a systematic presentation of Quantum Field Theory from first principles, emphasizing both theoretical concepts and experimental applications. Starting from introductory quantum and classical mechanics, this book develops the quantum field theories that make up the "Standard Model" of elementary processes. It derives the basic techniques and theorems that underly theory and experiment, including those that are the subject of theoretical development. Special attention is also given to the derivations of cross sections relevant to current high-energy experiments and to perturbative quantum chromodynamics, with examples drawn from electron-positron annihilation, deeply inelastic scattering and hadron-hadron scattering. The first half of the book introduces the basic ideas of field theory. The discussion of mathematical issues is everywhere pedagogical and self contained. Topics include the role of internal symmetry and relativistic invariance, the path integral, gauge theories and spontaneous symmetry breaking, and cross sections in the Standard Model and the parton model. The material of this half is sufficient for an understanding of the Standard Model and its basic experimental consequences. The second half of the book deals with perturbative field theory beyond the lowest-order approximation. The issues of renormalization and unitarity, the renormalization group and asymptotic freedom, infrared divergences in quantum electrodynamics and infrared safety in quantum chromodynamics, jets, the perturbative basis of factorization at high energy and the operator product expansion are discussed. Exercises are included for each chapter, and several appendices complement the text.
  

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Contents

SCALAR FIELDS
3
12 Relativistic scalar fields
5
13 Invariance and conservation
10
14 Lie groups and internal symmetries
16
15 The Poincaré group and its generators
20
Exercises
26
Canonical quantization
29
22 Quantum symmetries
32
92 Wick rotation in perturbation theory
250
93 Dimensional regularization
252
94 Poles at 𝑛 4
261
95 Timeordered perturbation theory
266
96 Unitarity
271
Exercises
278
Introduction to renormalization
280
102 Power counting and renormalizability
288

23 The free scalar field as a system of harmonic oscillators
38
24 Particles and Green functions
46
25 Interacting fields and scattering
49
Exercises
55
Path integrals perturbation theory and Feynman rules
58
32 The path integral and coherent states
71
33 Coherent state construction of the path integral in field theory
76
34 Feynman diagrams and Feynman rules
82
Exercises
92
Scattering and cross sections for scalar fields
94
42 The 𝑆matrix
98
43 Cross sections
100
44 The charged scalar Held
107
Exercises
114
Spinors vectors and gauge invariance
119
52 Spinor equations and Lagrangians
125
53 Vector fields and Lagrangians
131
54 Interactions and local gauge invariance
134
Exercises
144
Spin and canonical quantization
147
62 Unitary representations of the Poincaré group
148
63 Solutions with mass
152
64 Massless solutions
158
65 Quantization
162
66 Parity and leptonic weak interactions
170
Exercises
174
Path integrals for fermions and gauge fields
176
72 Fermions in an external field
182
73 Gauge vectors and ghosts
189
74 Reduction formulas and cross sections
199
Exercises
203
Gauge theories at lowest order
204
82 Cross sections with photons
217
83 Weak interactions of leptons
223
84 Quantum chromodynamics and quarkquark scattering
227
85 Gluons and ghosts
231
86 Partonmodel interpretation of QCD cross sections
237
Exercises
242
PART III REMORMALIZATION
247
103 Oneloop counterterms for ϕ³₆
290
104 Renormalization at two loops and beyond
300
105 Introduction to the renormalization group
309
Exercises
317
Renormalization and unitarity of gauge theories
319
112 Renormalization and unitarity in QED
334
113 Ward identities and the 𝑆matrix in QCD
348
114 The axial anomaly
358
Exercises
364
THE NATURE OF PRETURBATIVE CROSS SECTIONS
369
122 Ordera infrared bremsstrahlung
378
123 Infrared divergences to all orders
384
124 Infrared safety and renormalization in QCD
394
125 Jet cross sections at order 𝑎 in 𝐞𝐞 annihilation
404
Exercises
408
Analytic structure and infrared finiteness
411
132 The twopoint function
417
133 Massless particles and infrared power counting
422
134 The threepoint function and collinear power counting
431
135 The KinoshitaLeeNauenberg theorem
440
Exercises
447
Factorization and evolution in highenergy scattering
449
142 Deeply inelastic scattering for massless quarks
454
143 Factorization and parton distributions
459
144 Evolution
475
145 The operator product expansion
484
Exercises
490
Epilogue Bound states and the limitations of perturbation theory
492
APPENDICES
502
Symmetry factors and generating functionals
509
The standard model
514
T C and CPT
523
The Goldstone theorem and 𝛑⁰2𝑦
532
Groups algebras and Dirac matrices
539
Cross sections and Feynman rules
545
References
551
Index
562
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About the author (1993)

Sterman is affiliated with the Institute for Theoretical Physics at the State University of New York at Stony Brook.

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