Quantum field theory

659 Pages·2007·3.192 MB·English

by  Mark Srednicki

P1:RNK/XXX P2:RNK/XXX QC:RNK/XXX T1:RNK
CUUK761-Srednicki August25,2006 15:35
QUANTUM FIELD THEORY
Quantum field theory is the basic mathematical framework that is used to
describe elementary particles. It is a cornerstone of modern physics.
This textbook provides a complete and essential introduction to this sub-
ject.Assumingonlyanundergraduateknowledgeofquantummechanicsand
special relativity, it is ideal for graduate students beginning the study of ele-
mentary particles, and will also be of value to those in related fields such as
condensed-matter physics.
The step-by-step presentation begins with basic concepts illustrated by
simple examples, and proceeds through historically important results to
thorough treatments of modern topics such as the renormalization group,
spinor-helicitymethodsforquarkandgluonscattering,magneticmonopoles,
instantons, supersymmetry, and the unification of forces.
The book is written in a modular format, with each chapter as self-
contained as possible, and with the necessary prerequisite material clearly
identified. This structure results in great flexibility, and allows read-
ers to easily reach topics of specific interest. The book is based on a
year-long course given by the author and contains extensive problems,
with password-protected solutions available to lecturers at www.cambridge.
org/9780521864497.
Mark Srednicki is Professor of Physics at the University of California,
Santa Barbara. He gained his undergraduate degree from Cornell University
in 1977, and received a PhD from Stanford University in 1980. Professor
Srednicki has held postdoctoral positions at Princeton University and the
European Organization for Nuclear Research (CERN).
i
P1:RNK/XXX P2:RNK/XXX QC:RNK/XXX T1:RNK
CUUK761-Srednicki August25,2006 15:35
ii
P1:RNK/XXX P2:RNK/XXX QC:RNK/XXX T1:RNK
CUUK761-Srednicki August25,2006 15:35
QUANTUM FIELD THEORY
MARK SREDNICKI
University of California, Santa Barbara
iii
P1:RNK/XXX P2:RNK/XXX QC:RNK/XXX T1:RNK
CUUK761-Srednicki August25,2006 15:35
cambridge university press
Cambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,S˜aoPaulo
CambridgeUniversityPress
TheEdinburghBuilding,CambridgeCB22RU,UK
PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork
www.cambridge.org
Informationonthistitle:www.cambridge.org/9780521864497
(cid:1)C M.Srednicki2007
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithout
thewrittenpermissionofCambridgeUniversityPress.
Firstpublished2007
PrintedintheUnitedKingdomattheUniversityPress,Cambridge
A catalog record for this publication is available from the British Library
Library of Congress Cataloging in Publication data
ISBN-13 978-0-521-86449-7hardback
ISBN-10 0-521-86449-6hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof
URLsforexternalorthird-partyinternetwebsitesreferredtointhispublication,
anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,
accurateorappropriate.
iv
P1:RNK/XXX P2:RNK/XXX QC:RNK/XXX T1:RNK
CUUK761-Srednicki August25,2006 15:35
To my parents
Casimir and Helen Srednicki
with gratitude
v
P1:RNK/XXX P2:RNK/XXX QC:RNK/XXX T1:RNK
CUUK761-Srednicki August25,2006 15:35
vi
P1:RNK/XXX P2:RNK/XXX QC:RNK/XXX T1:RNK
CUUK761-Srednicki August25,2006 15:35
Contents
Preface for students page xi
Preface for instructors xv
Acknowledgments xx
Part I Spin zero 1
1 Attempts at relativistic quantum mechanics 3
2 Lorentz invariance (prerequisite: 1) 15
3 Canonical quantization of scalar fields (2) 22
4 The spin-statistics theorem (3) 31
5 The LSZ reduction formula (3) 35
6 Path integrals in quantum mechanics 43
7 The path integral for the harmonic oscillator (6) 50
8 The path integral for free field theory (3, 7) 54
9 The path integral for interacting field theory (8) 58
10 Scattering amplitudes and the Feynman rules (5, 9) 73
11 Cross sections and decay rates (10) 79
12 Dimensional analysis with h¯ = c = 1 (3) 90
13 The Lehmann–Ka¨ll´en form of the exact propagator (9) 93
14 Loop corrections to the propagator (10, 12, 13) 96
15 The one-loop correction in Lehmann–Ka¨ll´en form (14) 107
16 Loop crrections to the vertex (14) 111
17 Other 1PI vertices (16) 115
18 Higher-order corrections and renormalizability (17) 117
19 Perturbation theory to all orders (18) 121
20 Two-particle elastic scattering at one loop (19) 123
21 The quantum action (19) 127
22 Continuous symmetries and conserved currents (8) 132
23 Discrete symmetries: P, T, C, and Z (22) 140
24 Nonabelian symmetries (22) 146
vii
P1:RNK/XXX P2:RNK/XXX QC:RNK/XXX T1:RNK
CUUK761-Srednicki August25,2006 15:35
viii Contents
25 Unstable particles and resonances (14) 150
26 Infrared divergences (20) 157
27 Other renormalization schemes (26) 162
28 The renormalization group (27) 169
29 Effective field theory (28) 176
30 Spontaneous symmetry breaking (21) 188
31 Broken symmetry and loop corrections (30) 192
32 Spontaneous breaking of continuous symmetries (22, 30) 198
Part II Spin one half 203
33 Representations of the Lorentz group (2) 205
34 Left- and right-handed spinor fields (3, 33) 209
35 Manipulating spinor indices (34) 216
36 Lagrangians for spinor fields (22, 35) 221
37 Canonical quantization of spinor fields I (36) 232
38 Spinor technology (37) 237
39 Canonical quantization of spinor fields II (38) 244
40 Parity, time reversal, and charge conjugation (23, 39) 252
41 LSZ reduction for spin-one-half particles (5, 39) 261
42 The free fermion propagator (39) 267
43 The path integral for fermion fields (9, 42) 271
44 Formal development of fermionic path integrals (43) 275
45 The Feynman rules for Dirac fields (10, 12, 41, 43) 282
46 Spin sums (45) 291
47 Gamma matrix technology (36) 294
48 Spin-averaged cross sections (46, 47) 298
49 The Feynman rules for Majorana fields (45) 303
50 Massless particles and spinor helicity (48) 308
51 Loop corrections in Yukawa theory (19, 40, 48) 314
52 Beta functions in Yukawa theory (28, 51) 324
53 Functional determinants (44, 45) 327
Part III Spin one 333
54 Maxwell’s equations (3) 335
55 Electrodynamics in Coulomb gauge (54) 339
56 LSZ reduction for photons (5, 55) 344
57 The path integral for photons (8, 56) 349
58 Spinor electrodynamics (45, 57) 351
59 Scattering in spinor electrodynamics (48, 58) 357
60 Spinor helicity for spinor electrodynamics (50, 59) 362
61 Scalar electrodynamics (58) 371
P1:RNK/XXX P2:RNK/XXX QC:RNK/XXX T1:RNK
CUUK761-Srednicki August25,2006 15:35
Contents ix
62 Loop corrections in spinor electrodynamics (51, 59) 376
63 The vertex function in spinor electrodynamics (62) 385
64 The magnetic moment of the electron (63) 390
65 Loop corrections in scalar electrodynamics (61, 62) 394
66 Beta functions in quantum electrodynamics (52, 62) 403
67 Ward identities in quantum electrodynamics I (22, 59) 408
68 Ward identities in quantum electrodynamics II (63, 67) 412
69 Nonabelian gauge theory (24, 58) 416
70 Group representations (69) 421
71 The path integral for nonabelian gauge theory (53, 69) 430
72 The Feynman rules for nonabelian gauge theory (71) 435
73 The beta function in nonabelian gauge theory (70, 72) 439
74 BRST symmetry (70, 71) 448
75 Chiral gauge theories and anomalies (70, 72) 456
76 Anomalies in global symmetries (75) 468
77 Anomalies and the path integral for fermions (76) 472
78 Background field gauge (73) 478
79 Gervais–Neveu gauge (78) 486
80 The Feynman rules for N ×N matrix fields (10) 489
81 Scattering in quantum chromodynamics (60, 79, 80) 495
82 Wilson loops, lattice theory, and confinement (29, 73) 507
83 Chiral symmetry breaking (76, 82) 516
84 Spontaneous breaking of gauge symmetries (32, 70) 526
85 Spontaneously broken abelian gauge theory (61, 84) 531
86 Spontaneously broken nonabelian gauge theory (85) 538
87 The standard model: gauge and Higgs sector (84) 543
88 The standard model: lepton sector (75, 87) 548
89 The standard model: quark sector (88) 556
90 Electroweak interactions of hadrons (83, 89) 562
91 Neutrino masses (89) 572
92 Solitons and monopoles (84) 576
93 Instantons and theta vacua (92) 590
94 Quarks and theta vacua (77, 83, 93) 601
95 Supersymmetry (69) 610
96 The minimal supersymmetric standard model (89, 95) 622
97 Grand unification (89) 625
Bibliography 636
Index 000
P1:RNK/XXX P2:RNK/XXX QC:RNK/XXX T1:RNK
CUUK761-Srednicki August25,2006 15:35
x