The Physics Of Elementary Particles

The Physics Of Elementary Particles......Page 1
Half-Title......Page 2
Title-Page......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 16
1.1(a) Electrons To Pions......Page 18
1.1(b) Kaons And Hyperons......Page 21
1.2 The Neutrino......Page 24
1.3(a) The "Strong" Conservation Laws......Page 26
1.3(b) The Conservation Of Parity......Page 27
1.3(c) The Failure Of Parity Conservation......Page 29
1.3(d) The Conservation Of Isospin......Page 30
1.4(a) Associated Production......Page 31
1.4(b) Isospin And Strange Particles......Page 32
1.4(c) The Strangeness Quantum Number......Page 35
1.5 On The Existence Of Further Particles......Page 37
2.2 The Measurement Of Mass......Page 40
2.3 The Measurement Of Lifetime......Page 42
2.4(b) The Spin Of The Pion......Page 43
2.4(c) The Spin Of The Leptons......Page 45
2.4(d) The Helicity Of The Neutrino......Page 46
2.4(e) The Spins Of The Kaons And Hyperons......Page 48
2.5(b) The Gyromagnetic Ratio Of The Proton......Page 50
2.5(d) The Proton Magnetic Moment In Bohr Magnetons......Page 52
3.1 Introduction And Statement Of The Problem......Page 55
3.2(b) Intervals......Page 56
3.2(c) Invariance Properties Of The Interval......Page 57
3.2(d) Time And Space-Like Intervals......Page 58
3.2(e) The Transformation Of Coordinate Systems......Page 59
3.2(f) Four-Vectors......Page 61
3.2(g) The Energy-Momentum Four-Vector......Page 62
3.2(h) Coordinate Systems For The Energy-Momentum Vector......Page 63
3.2(i) Four-Tensors And Their Properties......Page 65
3.2(j) Classification Of The Lorentz Transformations......Page 67
3.2(k) Integration In Four-Dimensional Space......Page 69
3.3 Relativistic Wave Equations......Page 70
3.3(a) The Klein-Gordon Equation......Page 71
3.3(b) The Dirac Equation......Page 73
3.3(c) Covariant Form Of The Dirac Equation......Page 75
3.3(d) Some Properties Of The Gamma-Matrices......Page 76
3.3(e) The Spin Of A Dirac Particle......Page 79
3.3(f) The Magnetic Moment Of A Dirac Particle......Page 81
3.3(g) Solutions Of The Dirac Equation......Page 83
3.3(i) Normalisation Of The Dirac Equation......Page 88
3.3(j) Orthogonality Conditions For The Dirac Spinors......Page 91
3.3(k) Projection Operators For The Dirac Spinors......Page 92
3.3(l) The Dirac Equation For Particles Of Zero Mass......Page 94
3.3(m) Lorentz Transformations And The Dirac Equation......Page 97
3.3(n) Behavior Of The Linear Transformation Operator S......Page 98
3.3(o) Parity And The Dirac Wave Function......Page 100
3.3(p) The Dirac Bilinear Covariants......Page 102
3.4(a.1) Justification Of The Lagrangian Method......Page 105
3.4(a.2) Derivation Of The Euler-Lagrange Equation Of Motion......Page 106
3.4(b) Generalized Momenta And Hamilton's Equation Of Motion......Page 108
3.4(c.1) The Transition To A Continuous System......Page 109
3.4(c.2) The Transition To A Relativistic Equation......Page 111
3.4(d) The Energy And Momentum Of A Field......Page 113
3.4(e) Invariance Principles And Conservation Laws--Noether's Theorem......Page 114
3.4(f.1) Conservation Of Energy And Momentum......Page 116
3.4(f.2) Invariance Under Gauge Transformations......Page 117
4.1(b) State Vectors And Hilbert Space......Page 119
4.1(c) Operators......Page 123
4.1(d) The Multiplication Of Operators......Page 126
4.1(e) Some Properties Of The Unitary Operator......Page 127
4.1(f.1) The Schrodinger Representation......Page 130
4.1(f.2) The Heisenberg Representation......Page 131
4.1(g) Conservation Laws In Quantum Mechanical Systems......Page 133
4.2(b) Types Of Quantized Field Theories......Page 134
4.3(a) The Single Component Hermitian Field......Page 135
4.3(b) The Plane Wave Representation Of Phi......Page 136
4.3(c) Quantisation Of The Scalar Field......Page 139
4.3(d) The Occupation Number Operator......Page 141
4.3(e) The Decomposition Of The Scalar Field Into Spherical Waves......Page 143
4.3(f) Total Energy And Momentum Operators For The Scalar Field......Page 145
4.3(g) Displacement Operators And The Scalar Field......Page 149
4.3(h) The Non-Hermitian Scalar Field......Page 150
4.3(i) The Physical Interpretation Of The Non-Hermitian Scalar Field......Page 152
4.3(i.1) The Charge Operator For The Field......Page 153
4.3(i.2) The Total Energy And Momentum Operators......Page 156
4.4(a) The Classical Electromagnetic Field......Page 157
4.4(b) The Electromagnetic Field Tensor......Page 161
4.4(c) Lagrangians For The Vector Field......Page 162
4.4(d) Plane Wave Representation For The Electromagnetic Field......Page 163
4.4(e) Quantisation Of The Electromagnetic Field......Page 166
4.4(f) Physical Interpretation Of The Electromagnetic Field Operators......Page 167
4.5(a) The Plane Wave Representation......Page 169
4.5(b) The Hamiltonian Operator For The Dirac Field......Page 173
4.5(c) The Quantisation Of The Dirac Field......Page 175
4.5(d) Charge And Current Operators For The Dirac Field---Symmetrisation......Page 177
4.6(a) Introduction......Page 180
4.6(b) Scalar Fields......Page 181
4.6(c) Some Properties Of The Function Delta(x-x')......Page 182
4.6(d) Properties Of The Associated Delta-Functions......Page 185
4.6(e) Vacuum Expectation Values And The Delta-Functions......Page 187
4.6(f) Advanced And Retarded Delta-Functions......Page 191
4.6(g) Commutation Relations For The Electromagnetic Field......Page 192
4.6(h) Commutation Relations For The Dirac Field......Page 193
4.6(i) Vacuum Expectation Values For The Dirac Current Operator......Page 197
5.1(a) Introduction......Page 200
5.1(b) Continuous Transformations......Page 201
5.1(c) Discrete Transformations......Page 202
5.2 Gauge Transformations......Page 203
5.3(a) Introduction......Page 205
5.3(b) The Angular Momentum Operator......Page 208
5.3(c) The Angular Momentum Operators For The Klein-Gordon Field......Page 210
5.3(d) Angular Momentum Operators For The Electromagnetic Field......Page 211
5.3(e) Vectorial Addition Of Angular Momentum......Page 214
5.3(f) Angular Momentum Functions For The Electromagnetic Field......Page 218
5.3(g) Angular Momentum Operators For The Spinor Field......Page 219
5.4(a) Introduction......Page 221
5.4(b) Scalar And Pseudoscalar Fields......Page 222
5.4(c) The Electromagnetic Field......Page 225
5.4(d) The Inversion Of The Dirac Field......Page 228
5.5(b) Scalar And Pseudoscalar Fields......Page 232
5.5(c) The Charge Conjugation Of Self-Conjugate Fields......Page 235
5.5(d) The Dirac Field......Page 236
5.6(a) Introduction......Page 240
5.6(b) Time Reversal And Scalar Fields......Page 242
5.6(c) The Electromagnetic Field......Page 244
5.6(d) The Dirac Field......Page 245
5.7 Combined Reflections......Page 248
6.1(a) The Scattering Of Spinless Particles......Page 251
6.1(b) Phase Shifts And Scattering Functions......Page 256
6.1(c) Scattering From A "Black Sphere"......Page 257
6.1(d) The Scattering Of Particles With Spin......Page 259
6.2(b) The Quantum Mechanics Of Polarised Beams......Page 264
6.2(c) Composite Spin Space......Page 266
6.2(d) The Scattering Matrix......Page 268
6.2(e) ThePolarisation Induced In The Scattering Of Spin-1/2 Particles By A Spin-0 Target......Page 269
6.2(f) The Principle Of The Double Scattering Experiment......Page 271
6.2(g) The Scattering Of Relativistic Particles......Page 273
6.3(b) The Scattering Amplitude In The Born Approximation......Page 274
6.3(c) The Relationship Between Phase Shifts And Potentials......Page 277
6.3(d) The Behavior Of The Scattering Amplitudes And Phase Shifts At Low Momenta......Page 278
7.2 The S-Matrix......Page 280
7.3(b) The Invariance Properties Of The Transition Amplitude......Page 282
7.4(a) Basic Equations......Page 283
7.4(b.1) The Relative Velocity......Page 288
7.4(b.2) The Density Of Final States......Page 289
7.4(c) Cross-Sections For Processes Of The Type a+b To d+e......Page 295
7.4(d) The Summation Over States Of Polarisation......Page 296
7.5(a) The Relationship Between The Scattering And Transition Amplitudes......Page 300
7.5(b) Multichannel Reactions......Page 301
7.5(c) The Unitarity Of The S-Matrix And The Optical Theorem......Page 302
8.1(a) Introduction......Page 306
8.1(b) The Relationship Between The Heisenberg And The Interaction Representations......Page 308
8.1(c) The S-Matrix In The Interaction Representation......Page 309
8.2(a) Introduction......Page 311
8.2(b) Chronological Products And The S-Matrix......Page 312
8.2(c) Bare And Physical States--The Adiabatic Hypothesis......Page 314
8.2(d) A Comparison With Time-Dependent Perturbation Theory......Page 316
8.2(e) The Transition Probability In Time-Dependent Perturbation Theory--Fermi's "Golden Rule"......Page 319
8.3(a) Equations Of Motion For Interacting Systems......Page 320
8.3(b) The Relationship Between The Hamiltonian And Lagrangian Densities For Interacting Systems......Page 322
8.3(c) The S-Matrix Expansion For The Photon-Electron Interaction......Page 323
8.4(a) The Normal Ordering Operator And Normal Products......Page 325
8.4(b) Proof Of The Theorem For Normal Ordering......Page 328
8.5(a) Introduction......Page 329
8.5(b) Feynman Graphs......Page 334
8.5(c) Chronological Ordering Of The Operators......Page 336
8.5(d) Graphs In Momentum Space......Page 337
8.6(a) A Specific Example--Compton Scattering......Page 339
8.6(b) Summary Of  Rules For Evaluating Graphs In Momentum Space......Page 342
8.6(c) Examples Of The Formation Of Matrix Elements......Page 345
8.6(d) The Substitution Law......Page 346
8.7(a) Introduction......Page 347
8.7(b) Pion-Nucleon Scattering......Page 348
8.7(c) The Beta-Decay Of The Neutron......Page 351
8.8(a) Introduction......Page 354
8.8(b) The Axiomatic Formulation Of Field Theory--The "In' And "Out" Operators......Page 355
8.8(c) The Axiomatic Formulation--Definitions......Page 357
8.9(b) The S-Matrix In Terms Of Retarded Commutators......Page 361
8.9(c) Spinor Fields......Page 367
9.1 Introduction......Page 369
9.2(a) Introduction......Page 370
9.2(b) Construction Of Interaction Terms......Page 372
9.2(c) Reflections And Strong Interactions......Page 375
9.2(d) Experimental Limits On P, T, C Invariance In Strong And Electromagnetic Interactions......Page 376
9.2(e) Invariance Principles And Weak Interactions......Page 381
9.2(f) The CTP Theorem......Page 383
9.2(g) Some Consequences Of The Spin-Statistics Relationship......Page 384
9.2(h) The Masses And Lifetimes Of Chage Conjugate Particles......Page 386
9.3(a) Introduction......Page 389
9.3(b) Gauge Invariance And The Electromagnetic Interaction......Page 390
9.3(c) The Principle Of Minimal Electromagnetic Interaction......Page 391
9.3(d) The Conservation Of Fermions......Page 392
9.4(a) Charge Independence In Strong Interactions......Page 395
9.4(b) Transformations In Isospin Space......Page 397
9.4(c) The Pion-Nucleon Interaction (1)......Page 402
9.4(d) The Pion-Nucleon Interaction (2)......Page 403
9.4(f) The Principle Of Extended Symmetry......Page 407
9.4(g) G Conjugation And Isospin Space......Page 409
9.4(h) Hypercharge And Strangeness......Page 412
9.5(b) The Properties Of The Pions......Page 414
9.5(c) Decay Processes Yielding Three Pions......Page 416
10.1 Introduction......Page 422
10.2(a) Mathematical Preliminaries......Page 423
10.2(b) Basic Forms For The Dispersion Relations......Page 427
10.2(c) Causality And The Dispersion Relations......Page 431
10.2(d) Dispersion Relations In Classical Physics--The Kramers-Kronig Relation......Page 433
10.2(e) Difference Formulae And Convergence......Page 436
10.3(b) Crossing Symmetry And Other Properties......Page 438
10.3(c) The Analytic Properties Of T(Omega)......Page 440
10.3(d) Physical And Unphysical Regions In The Forward Scattering Dispersion Relation......Page 443
10.3(e) The Unphysical Region And The Scattering Of Scalar Particles......Page 446
10.3(f) Dispersion Relations For The Forward Scattering Of The Pion-Nucleon System......Page 450
10.3(g) An Application Of A Dispersion Relation......Page 454
10.4(b) Kinematic Features......Page 455
10.4(c) Physical Processes And Variables s, t, u......Page 457
10.4(d) The Mandelstam Conjecture......Page 460
10.4(e) Pole Terms And "Polology"......Page 463
10.5(a) Introduction......Page 467
10.5(b) Regge Poles......Page 468
10.5(c) Resonances And Regge Trajectories......Page 469
10.5(d) The Scattering Amplitude At High Energy......Page 472
10.5(e) Rules For Constructing The Transition Amplitude......Page 476
10.5(f) The Factoring Principle......Page 478
11.1(a) Kinematics......Page 480
11.1(b) Sum Over Polarisation States......Page 482
11.1(c) The Properties Of The Scattered Photon Beam......Page 487
11.1(d) Comparison With Experiment......Page 490
11.1(e) Compton Scattering By Protons......Page 491
11.2(a) Moller Scattering......Page 493
11.2(b) Bhabha Scattering......Page 497
11.2(c) The Annihilation Of Free Electron-Positron Pairs......Page 501
11.2(d) Positronium......Page 507
11.3(a) Introduction......Page 512
11.3(b) Ultraviolet Divergences......Page 514
11.3(c) The Self-Energy Of An Electron......Page 515
11.3(e) Consequences of The Higher Terms And The Limits Of Validity Of Quantum Electrodynamics......Page 520
11.4(b) Form Factors......Page 525
11.4(c) Invariance Properties And Form Factors......Page 528
11.4(d) Form Factors For The Proton And Neutron......Page 531
11.4(e) The Evaluation Of The Form Factors From The Experimental Data......Page 532
11.4(f) Interpretation Of The Form Factors......Page 537
12.1 Introduction......Page 543
12.2(a) Nuclear Beta-Decay--Selection Rules......Page 544
12.2(b) Parity Independent Forms Of The Matrix Element For Beta-Decay......Page 546
12.2(c) Parity Failure And The Matrix Element For Beta-Decay......Page 553
12.2(d) The Relative Signs Of The Coupling Terms V And A......Page 558
12.3 Muon Decay......Page 561
12.5(a) Introduction......Page 569
12.5(b) The Delta S=0 Leptonic Transitions......Page 570
12.6(a) Introduction......Page 572
12.6(b) Tests Of The Conserved Vector Current Hypothesis......Page 575
12.7 Pion Decay......Page 578
12.8(a) Structure Of The Matrix Element......Page 581
12.8(b) Experimental Data......Page 583
12.8(c) Universality In The Strangeness Conserving Weak Interactions......Page 585
12.9(a) Introduction......Page 586
12.9(b) The Process Kaon To Pion-Lepton-Neutrino......Page 588
12.9(c) Isospin Changes In The Leptonic Decays Of Strange Particles......Page 589
12.9(d) The Neutral Kaons......Page 590
12.9(e) The Decay Process Neutral Kaon To Electron/Positron-Plus/Minus Pions-Neutrino......Page 594
12.10(a) Hyperon Decay......Page 595
12.10(b) Isospin Changes And The Nonleptonic Decay Of The Hyperons......Page 599
12.10(c) The Nonleptonic Decay Of Kaons And Isospin Changes......Page 601
12.11 The Intermediate  Boson Hypothesis......Page 602
12.12 Neutrino Induced Reactions......Page 606
13.1 Introduction......Page 611
13.2 The Nucleon Isobars......Page 612
13.3(a) The Rho-System......Page 616
13.3(b) The Omega-System......Page 619
13.3(c) The Eta-System......Page 620
13.4(a) The Parity Of The Nonresonant States......Page 621
13.4(b) The Strange Particle Resonance States......Page 623
13.5(a) Unitary Symmetry......Page 628
13.5(a.1) Elements Of Group Theory......Page 629
13.5(a.2) Group Theory And The Unitary Transformation......Page 630
13.5(a.3) The SU(2) Group......Page 633
13.5(a.4) The SU(3) Group......Page 634
13.5(a.5) The Mass Formula......Page 639
13.5(b) Dynamical Models (1). Bound States......Page 642
13.5(b) Dynamical Models (2). Regge Poles And Trajectories......Page 644
14.1(a) Introduction......Page 646
14.1(b) Partial Wave Analysis Of The Data Below 250MeV In Pion-Nucleon Scattering......Page 647
14.1(c) Interpretation Of The Low Energy Scattering Data......Page 653
14.1(d) The Photoproduction Of Pions At Low Energies......Page 663
14.1(e) The Higher Nucleon Resonances......Page 668
14.2(a) Polarisation And Related Parameters......Page 672
14.2(b) Phase Shifts For Elastic Nucleon-Nucleon Scattering......Page 678
14.2(c) Interpretation Of The Scattering Data......Page 680
14.3(a) Nucleon-Nucleon Inelastic Scattering......Page 683
14.3(b) Pion-Nucleon Inelastic Scattering......Page 687
14.4(a) Scattering Data......Page 691
14.4(b) The Annihilation Of Antiprotons At Rest......Page 693
14.5(a) The Production Of Strange Particles......Page 695
14.5(b) Total Cross-Sections For Kaon-Proton Scattering......Page 696
14.5(c) +Kaon-Nucleon Scattering......Page 697
14.5(d) The Kaon-Proton Interaction At Low Energies......Page 699
14.5(e) The Hyperon-Nucleon Interaction......Page 703
14.6(a) Data On Total Cross-Sections......Page 704
14.6(b) Regge Poles And Total Cross-Sections......Page 706
14.6(c) Elastic And Inelastic Cross-Sections......Page 709
A.1 Notation......Page 711
A.2 Units......Page 712
A.3(a) Introduction......Page 713
A.3(b) Matrix Addition And Multiplication......Page 714
A.3(c) Special Matrices......Page 715
A.3(d) Evaluation Of Matrices......Page 716
A.4 Tensors......Page 717
A.5 Gamma-Matrices......Page 718
A.6 Delta Functions......Page 720
A.7 Spherical Functions......Page 721
A.7(b) Spherical Harmonics......Page 722
A.7(c) The Vector Addition Of Angular Momenta......Page 724
A.7(d) Projection Operators......Page 725
A.8 Coordinate Systems......Page 730
A.9.1 Atomic Constants......Page 732
A.9.2 Particle Data......Page 733
A.9.3 Resonant States......Page 734
A.9.4 Weak Decay Modes......Page 735
References......Page 736
Index......Page 748