Quantum Field Theory And The Standard Model

Quantum Field Theory And The Standard Model......Page 1
Half-Title......Page 3
Title-Page......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 17
Part I Field theory......Page 21
1.1 Blackbody radiation......Page 23
1.2 Einstein coefficients......Page 25
1.3 Quantum field theory......Page 27
2.1 Lorentz invariance......Page 30
2.2 Classical plane waves as oscillators......Page 37
2.3 Second quantization......Page 40
 Problems......Page 47
3.1 Hamiltonians and Lagrangians......Page 49
3.2 The Euler–Lagrange equations......Page 51
3.3 Noether's theorem......Page 52
3.4 Coulomb's law......Page 57
3.5 Green's functions......Page 59
 Problems......Page 62
4 Old-fashioned perturbation theory......Page 66
4.1 Lippmann–Schwinger equation......Page 67
4.2 Early infinities......Page 72
 Problems......Page 75
5 Cross sections and decay rates......Page 76
5.1 Cross sections......Page 77
5.2 Non-relativistic limit......Page 83
5.3 e[sup(+)]e[sup(-)]→μ[sup(+)]μ[sup(-)] with spin......Page 85
 Problems......Page 87
6 The S-matrix and time-ordered products......Page 89
6.1 The LSZ reduction formula......Page 90
6.2 The Feynman propagator......Page 95
 Problems......Page 97
7 Feynman rules......Page 98
7.1 Lagrangian derivation......Page 99
7.2 Hamiltonian derivation......Page 104
7.3 Momentum-space Feynman rules......Page 113
7.4 Examples......Page 117
7.A Normal ordering and Wick's theorem......Page 120
 Problems......Page 123
Part II Quantum electrodynamics......Page 127
8.1 Unitary representations of the Poincaré group......Page 129
8.2 Embedding particles into fields......Page 133
8.3 Covariant derivatives......Page 140
8.4 Quantization and the Ward identity......Page 143
8.5 The photon propagator......Page 148
8.6 Is gauge invariance real?......Page 150
8.7 Higher-spin fields......Page 152
 Problems......Page 158
9.1 Quantizing complex scalar fields......Page 160
9.2 Feynman rules for scalar QED......Page 162
9.3 Scattering in scalar QED......Page 166
9.4 Ward identity and gauge invariance......Page 167
9.5 Lorentz invariance and charge conservation......Page 170
 Problems......Page 175
10 Spinors......Page 177
10.1 Representations of the Lorentz group......Page 178
10.2 Spinor representations......Page 183
10.3 Dirac matrices......Page 188
10.4 Coupling to the photon......Page 193
10.5 What does spin ½ mean?......Page 194
10.6 Majorana and Weyl fermions......Page 198
 Problems......Page 201
11 Spinor solutions and CPT......Page 204
11.1 Chirality, helicity and spin......Page 205
11.2 Solving the Dirac equation......Page 208
11.3 Majorana spinors......Page 212
11.4 Charge conjugation......Page 213
11.5 Parity......Page 215
11.6 Time reversal......Page 218
 Problems......Page 221
12 Spin and statistics......Page 225
12.1 Identical particles......Page 226
12.2 Spin-statistics from path dependence......Page 228
12.3 Quantizing spinors......Page 231
12.4 Lorentz invariance of the S-matrix......Page 232
12.5 Stability......Page 235
12.6 Causality......Page 239
 Problems......Page 243
13 Quantum electrodynamics......Page 244
13.1 QED Feynman rules......Page 245
13.2 γ-matrix identities......Page 249
13.3 e[sup(+)]e[sup(-)]→-μ[sup(+)]μ[sup(-)]......Page 250
13.4 Rutherford scattering e[sup(-)]p[sup(+)]→e[sup(-)]p[sup(+)]......Page 254
13.5 Compton scattering......Page 258
13.6 Historical note......Page 266
 Problems......Page 268
14.1 Introduction......Page 271
14.2 The path integral......Page 274
14.3 Generating functionals......Page 281
14.4 Where is the iε?
......Page 284
14.5 Gauge invariance......Page 287
14.6 Fermionic path integral......Page 289
14.7 Schwinger–Dyson equations......Page 292
14.8 Ward–Takahashi identity......Page 297
 Problems......Page 303
Part III Renormalization......Page 305
15.1 Casimir effect......Page 307
15.2 Hard cutoff......Page 309
15.3 Regulator independence......Page 311
15.4 Scalar field theory example......Page 316
 Problems......Page 319
16 Vacuum polarization......Page 320
16.1 Scalar ф[sup(3)] theory......Page 322
16.2 Vacuum polarization in QED......Page 324
16.3 Physics of vacuum polarization......Page 329
 Problems......Page 334
17.1 Extracting the moment......Page 335
17.2 Evaluating the graphs......Page 338
 Problems......Page 341
18 Mass renormalization......Page 342
18.1 Vacuum expectation values......Page 343
18.2 Electron self-energy......Page 344
18.3 Pole mass......Page 350
18.4 Minimal subtraction......Page 354
18.5 Summary and discussion......Page 356
 Problems......Page 358
19.1 Counterterms......Page 359
19.2 Two-point functions......Page 362
19.3 Three-point functions......Page 365
19.4 Renormalization conditions in QED......Page 369
19.5  Z[sub(1)]=Z[sub(2)]: implications and proof......Page 370
 Problems......Page 374
20 Infrared divergences......Page 375
20.1 e[sup(+)]e[sup(-)]→μ[sup(+)]μ[sup(-)] (+γ)......Page 376
20.2 Jets......Page 384
20.3 Other loops......Page 386
20.A Dimensional regularization......Page 393
 Problems......Page 400
21 Renormalizability......Page 401
21.1 Renormalizability of QED......Page 402
21.2 Non-renormalizable field theories......Page 406
 Problems......Page 413
22 Non-renormalizable theories......Page 414
22.1 The Schrödinger equation......Page 415
22.2 The 4-Fermi theory......Page 416
22.3 Theory of mesons......Page 420
22.4 Quantum gravity......Page 423
22.6 Mass terms and naturalness......Page 427
22.7 Super-renormalizable theories......Page 434
 Problems......Page 436
23 The renormalization group......Page 437
23.1 Running couplings......Page 439
23.2 Renormalization group from counterterms......Page 443
23.3 Renormalization group equation for the 4-Fermi theory......Page 446
23.4 Renormalization group equation for general interactions......Page 449
23.5 Scalar masses and renormalization group flows......Page 455
23.6 Wilsonian renormalization group equation......Page 462
 Problems......Page 470
24 Implications of unitarity......Page 472
24.1 The optical theorem......Page 473
24.2 Spectral decomposition......Page 486
24.3 Polology......Page 491
24.4 Locality......Page 495
 Problems......Page 497
Part IV The Standard Model......Page 499
25 Yang–Mills theory......Page 501
25.1 Lie groups......Page 502
25.2 Gauge invariance and Wilson lines......Page 508
25.3 Conserved currents......Page 513
25.4 Gluon propagator......Page 515
25.5 Lattice gauge theories......Page 523
 Problems......Page 526
26 Quantum Yang–Mills theory......Page 528
26.1 Feynman rules......Page 529
26.2 Attractive and repulsive potentials......Page 532
26.3 e[sup(+)]e[sup(-)]→hadrons and α[sub(s)]......Page 533
26.4 Vacuum polarization......Page 537
26.5 Renormalization at 1-loop......Page 541
26.6 Running coupling......Page 546
26.7 Defining the charge......Page 549
 Problems......Page 553
27 Gluon scattering and the spinor-helicity formalism......Page 554
27.1 Spinor-helicity formalism......Page 555
27.2 Gluon scattering amplitudes......Page 562
27.3 gg→gg......Page 565
27.4 Color ordering......Page 568
27.5 Complex momenta......Page 571
27.6 On-shell recursion......Page 575
27.7 Outlook......Page 578
 Problems......Page 579
28 Spontaneous symmetry breaking......Page 581
28.1 Spontaneous breaking of discrete symmetries......Page 582
28.2 Spontaneous breaking of continuous global symmetries......Page 583
28.3 The Higgs mechanism......Page 595
28.4 Quantization of spontaneously broken gauge theories......Page 600
 Problems......Page 603
29.1 Electroweak symmetry breaking......Page 604
29.2 Unitarity and gauge boson scattering......Page 608
29.3 Fermion sector......Page 612
29.4 The 4-Fermi theory......Page 622
29.5 CP violation......Page 625
 Problems......Page 634
30 Anomalies......Page 636
30.1 Pseudoscalars decaying to photons......Page 637
30.2 Triangle diagrams with massless fermions......Page 642
30.3 Chiral anomaly from the integral measure......Page 648
30.4 Gauge anomalies in the Standard Model......Page 651
30.5 Global anomalies in the Standard Model......Page 654
30.6 Anomaly matching......Page 658
 Problems......Page 660
31 Precision tests of the Standard Model......Page 661
31.1 Electroweak precision tests......Page 662
31.2 Custodial SU(2), ρ, S, T and U......Page 673
31.3 Large logarithms in flavor physics......Page 677
 Problems......Page 686
32 Quantum chromodynamics and the parton model......Page 687
32.1 Electron–proton scattering......Page 688
32.2 DGLAP equations......Page 697
32.3 Parton showers......Page 702
32.4 Factorization and the parton model from QCD......Page 705
32.5 Lightcone coordinates......Page 715
 Problems......Page 718
Part V Advanced topics......Page 721
33 Effective actions and Schwinger proper time......Page 723
33.1 Effective actions from matching......Page 724
33.2 Effective actions from Schwinger proper time......Page 725
33.3 Effective actions from Feynman path integrals......Page 731
33.4 Euler–Heisenberg Lagrangian......Page 733
33.5 Coupling to other currents......Page 742
33.6 Semi-classical and non-relativistic limits......Page 745
33.A Schwinger's method......Page 748
 Problems......Page 752
34 Background fields......Page 753
34.1 1PI effective action......Page 755
34.2 Background scalar fields......Page 763
34.3 Background gauge fields......Page 772
 Problems......Page 778
35 Heavy-quark physics......Page 780
35.1 Heavy-meson decays......Page 782
35.2 Heavy-quark effective theory......Page 785
35.3 Loops in HQET......Page 788
35.4 Power corrections......Page 792
 Problems......Page 795
36 Jets and effective field theory......Page 796
36.1 Event shapes......Page 798
36.2 Power counting......Page 800
36.3 Soft interactions......Page 802
36.4 Collinear interactions......Page 810
36.5 Soft-Collinear Effective Theory......Page 815
36.6 Thrust in SCET......Page 822
 Problems......Page 830
Appendices......Page 833
A.1 Dimensional analysis......Page 835
A.2 Signs......Page 837
A.3 Feynman rules......Page 839
A.4 Dirac algebra......Page 840
 Problems......Page 841
B.1 Integration parameters......Page 842
B.2 Wick rotations......Page 843
B.3 Dimensional regularization......Page 845
B.4 Other regularization schemes......Page 850
 Problems......Page 853
References......Page 854
Index......Page 862
Minor corrections (Unimportant errors in equations)......Page 871
Typos (Superficial formatting issues)......Page 875
Important corrections (Errors in derivations or results)......Page 879
Minor corrections (Unimportant errors in equations)......Page 880
Typos (Superficial formatting issues)......Page 882
Minor corrections (Unimportant errors in equations)......Page 884
Typos (Superficial formatting issues)......Page 886
Back Cover......Page 892