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1 Historical introduction 1
2 Quantized Dirac fields 7
2. Dirac equation
2.2 Representations of 7 matrices 9
2.3 Products of ' matrices 11
2.4 Relativistic covariance 13
2.5 Helicity 17
2.6 Gauge transformations 1
2.7 Chirality 18
.8 Solution of the Dirac equation 22
2.9 Quantization 31
210 Symmetry transformation of states 36
2.11 C, P, and T transformations 48
2.12 Wave packets 60
2 13 Finite normalization volume 63
2,14 Fierz transformations 64
3 The Standard Model 67
3. Electroweak Lagrangian 71
3.2 Electroweak interactions 75
3.3 Three generations 80
3 4 The Higgs mechanism 83
3.5 Fermion masses and mixing 88
3.6 Gauge bosons 97
.7 Effective low-energy CC and NC Lagrangians 102
4 Three-generation mixing 106
4.1 Diagonalization of the mass matrix 107
4.2 Physical parameters in the mixing matrix 108
4.3 Parameterization of the mixing matrix 109
4.4 Degenerate masses 116
4.5 Mixing matrix with one vanishing element 118
4.6 CP violation 120
4.7 Rephasing invariants 124
4.8 1 intarity triangles 1.2
4.9 Conditions for CP violation 133
5 Neutrino interactions 135
5.1. Neutrino-electron interactions 136
5.2 Hadron decays 147
5.3 Neutrino-nucleon scattering 160
6 Massive neutrinos 180
6.1 Dirac masses 180
6.2 Majorana neutrinos 188
6.3 Mixing of three Majorana neutrinos 208
6.4 One-generation Dirac-Majorana mass term 216
6.5 Three-generation Dirac-Miajorana mixing 229
6.6 Special cases 235
6. Majorana mass matrix 237
7 Neutrino oscillations in vacuum 245
7.1 Standard Derivation of the Neutrino Oscillation Probability 247
72 Antineutrino case 254
.3 CPT, CP, and T transformation 256
7.4 Tvwo-neutrino mixing 259
7.5 Types of neutrino oscillation experiments 261
Tv. A1 I 261
7.6 Averaged transition probability 267
17 Large A2 dominance 273
7 Active snall A Mn 277
8 Theory of neutrino oscillations in vacuum 283
4 Plane-wvae a,pproxinination 24
8,2 a:v e- packet treatment 299
8.3 Size of neutrino wave packets 311
8.4 Questions 316
9 Neutrino oscillations in matter 322
9.1 lEfecttiu potentials in matter 323
9.2 Evolution of nieutrino flarvors 329
9.3 The MSW effect 331
9.4 Slab approximation 339
9. 5 Parametric resonance 341
9.6 Geometrical representation 343
10 Solar neutrinos 352
10 F Th-ermonclear energy ipoduction 303
102 Standard solar models 359
10.3 M odei-independ ent constraints on solar neutrino fluxes 364
10.4 Honestake experirmne 366
10.5 Gallium experiments 368
10..6 \ater Cherenkov detectors 372
10(7 .Vacumm oscillafions 381
10.8 Resonant fiavor transitions in the Sun 382
10.9 Regneration of solar v,?s in the Earth 386
10.10 Global fit of solar neutrino data 389
11 Atmospheric neutrinos 390
11.1 Flux of atmospheric neutrinos 393
11.2 Atmospheric neutrino experiments 416
12 Terrestrial neutrino oscillation experiments 428
12.1 Sensitivity 429
12.2 Reactor experiments 432
12.3 Accelerator experiments 443
13 Phenomenology of three-neutrino mixing 452
13.1 Neutrino oscillations in vacuum 453
13.2 Matter effects 465
13.3 Analysis of oscillation data 474
14 Direct measurements of neutrino mass 484
14.1 Beta decay 485
14.2 Pion and tau decays 493
14.3 Neutrinoless double-beta decay 494
15 Supernova neutrinos 511
15A1. Supernova types 512
15.2 Supernova rates 515
15.3 Core-collapse supernova dynamics 517
15.4 SN1987A 528
I.5.5 iNeutrino mass 534
15.6 Neutrino mixing 535
15.7 Other neutrino properties 536
15.8 uture 537
1I Cosmology 540
16.1 Basic general relativity 540
16.2 Robertson-Walker metric 543
16.3 Dynamics of expansion 553
16.4 Matter-dominated Universe 560
16.5 Radiation-dominated Universe 562
16.6. Curvature-dominated Universe 563
16.7 Vacuum-dominated Universe 563
16.8 Thermodynamics of the early Universe 564
16.9 Entropy 569
16.10 Decoupling 572
16.11 Cosmic microwave background radiation 577
17 Relic neutrinos 586
17.1 Neutrino decoupling 587
17,2 Electron-positron annihilation 588
17.3 Neutrino temFpereature 589
17.4 Energy density of light massive neutrinos 590
17.5 Energy density of heavy neutrinos 591
17.6 Big-Bang nucleosynthesis 596
17.7 Large-scale structure formation 600
17.8 Global fits of cosmological data 612
17 .9 Number of neutrinos 618
17.10 Neutrino asymmetry 621
Appendices
A Conventions, useful formiulas, and physical constants 626
A. 1 Conventions 626
A.2 Pauli matrices 628
A.3 Dirac matrices 629
A.4 Mathematical formulas 634
A. P ysical constants 635
B Special relativity 63 7
B. 1 The Lorentz group 637
B12 Representations of the Lorentz group 643
B.3 The Poincar6 group and its representations 646
C Lagrangian theory 649
C.I Variational principle and field equations 649
C .2 Canonical quantization 650
C 3 Noethers theorem 650
C.4 Space-time translations 652
C.5 Lorentz transformations 653
C.o Clomplex fields 653
C.? Global gauge symmetry 654
D Gauge theories 657
D.I General formulation of gauge theories 657
"D.2 Quantum ch ronodynamics 662
E Feynnman rules of the standard electroweak model 664
E,1 External lines 664
E.2 Interna lines 665
E.3 Vertices 666
E.4 Cross-sections and decay rates 668