Introduction to Elementary Particle Theory (eBook)

International Series of Monographs In Natural Philosophy

Yu. V. Novozhilov (Autor)

D. ter Haar (Herausgeber)

eBook Download: PDF

2013 | 1. Auflage
400 Seiten
Elsevier Science (Verlag)
978-1-4831-8731-0 (ISBN)

Infos

Introduction to Elementary Particle Theory details the fundamental concepts and basic principles of the theory of elementary particles. The title emphasizes on the phenomenological foundations of relativistic theory and to the strong interactions from the S-matrix standpoint. The text first covers the basic description of elementary particles, and then proceeds to tackling relativistic quantum mechanics and kinematics. Next the selection deals with the problem of internal symmetry. In the last part, the title details the elements of dynamical theory. The book will be of great use to students and researchers in the field of particle physics.

Inhalt

Front Cover 
1 
Introduction to Elementary Particle Theory 
4 
Copyright Page 
5 
Table of Contents 
6 
PREFACE 10
AUTHOR'S PREFACE TO THE ENGLISH EDITION 12
TRANSLATOR'S PREFACE 13
NOMENCLATURE 14
PART I: INTRODUCTION: STATES OF ELEMENTARY PARTICLES 16
CHAPTER 1. ELEMENTS OF RELATIVISTIC QUANTUM THEORY 
18 
§ 1.1. Homogeneity of space-time and the Poincaré group 19
§ 1.2. Quantum mechanics and relativity 22
§ 1.3. Basis quantities 29
§ 1.4. Description of scattering. The S-matrix 34
CHAPTER 2. FOUNDATIONS OF PHENOMENOLOGICAL DESCRIPTION 
39 
§ 2.1. Interactions and internal symmetry 
40 
§ 2.2. Symmetry and particle classification 44
§ 2.3. Unstable particles 46
PART II: RELATIVISTIC KINEMATICS AND REFLECTIONS 
54 
CHAPTER 3. THE LORENTZ GROUP AND THE GROUP SL(2, c) 
56 
§ 3.1. Second-order imimodiilar matrices and the Lorentz transformation 56
§ 3.2. Spinors 61
§ 3.3. Irreducible representations and generalized spinor analysis 65
§ 3.4. Direct products of representations and covariant Clebsch-Gordan coefficients 70
§ 3.5. Representations of the unitary group SU2 
71 
CHAPTER 4. THE QUANTUM MECHANICAL POINCARÉ GROUP 
75 
§ 4.1. Introductory remarks 75
§ 4.2. Transfoimations and momenta. The little group and the Wigner operator 77
§ 4.3. Unitary representations. Case m2 > 0
82 
§ 4.4. Spinor functions and quantum fields for m2 > 0
88 
§ 4.5. Unitary representations in the case m = 0. Equations of motion 
93 
§ 4.6. Multi-particle states 99
CHAPTER 5. WAVE FUNCTIONS AND EQUATIONS OF MOTION FOR PARTICLES WITH ARBITRARY SPIN 
105 
§ 5.1. Wave functions, bilinear Hermitian forms, and equations of motion 106
§ 5.2. The Dirac equation 109
§ 5.3. 2(2J+ l)-component functions for spin J 
120 
§ 5.4· Particles with spin J = 1 122
§ 5.5. Rarita-Schwlnger wave functions 124
§ 5.6. Bargmann-Wigner wave functions 128
§ 5.7. The Duffin-Kemmer equation 131
CHAPTER 6. REFLECTIONS 
133 
§ 6.1. Total reflection ., or CPT 
134 
§ 6.2. The operations P, C, and . 144
§ 6.3. Reflections and interactions. Decays 151
§ 6.4. Summary of fonnolae for reflection transformations 157
CHAPTER 7. THE SCATTERING MATRIX. KINEMATICS 
161 
§ 7.1. The problem of kinematics 161
§ 7.2. The variables s, t, u 
163 
§ 7.3. Cross-sectíons for processes. Unitarity and optical theorem 168
§ 7.4. Helicity amplitudes 173
§ 7.5. Spinor amplitudes (M-functions) and invariant amplitudes 
177 
PART III: INTERNAL SYMMETRY 
188 
CHAPTER 8. ISOSPIN SYMMETRY 
190 
§ 8.1. Isospin multiplets, hypercharge, and the group SU2 190
§ 8.2. Isospin and reflections. Antiparticle states. G-parity 194
§ 8.3. Multi-particle states and isospin amplitudes. Decays and relations between reactions 
199 
CHAPTER 9. THE GROUP SU3 
205 
§ 9.1. The matrices .a and structure constants 
205 
§ 9.2. The fundamental representation and quarks. U- and V-spin 
208 
§ 9.3. Representations of the group SU3 211
CHAPTER 10. SU3 SYMMETRY AND THE CLASSIFICATION OF PARTICLES AND RESONANCES 
219 
§ 10.1. Unitary representations and multiplets 219
§ 10.2. Symmetry breaking and mass splitting 227
§ 10.3. Relations between transition amplitudes 230
§ 10.3. Relations between transition amplitudes 230
§ 10.4. The quark model 234
§ 10.5. SU6 multiplets 236
PART IV: ELEMENTS OF DYNAMICAL THEORY 
242 
CHAPTER 11. THE S-MATRIX, CURRENTS, ANÍD CROSSING SYMMETRY 
244 
§ 11.1. Interpolating fields, currents, and the reduction formula 244
§ 11.2· Crossing symmetry 250
§ 11.3. Crossing matrices for SU2 and SU3 
255 
§ 11.4. Properties of vertex parts 257
CHAPTER 12. ANALYTIC PROPERTIES OF THE SCATTERING AMPLITUDE 
262 
§ 12.1. Unitarity and the absorptive part 262
§ 12.2. Maximal analyticity 269
§ 12.3. Dispersion relations 272
§ 12.4. Partial wave amplitudes and fixed-energy dispersion relations. The Gribov-Froissart formula 
278 
§ 12.5. Analytic properties of form factors. The pion form factor 285
CHAPTER 13. ASYMPTOTIC BEHAVIOR OF THE SCATTERING AMPLITUDE AT HIGH ENERGIES. REGGE POLES 
292 
§ 13.1. Scattering at high energies (experiment) 292
§ 13.2. Bounds on the amplitude at high energies 296
§ 13.3. The Regge-pole hypothesis and the asymptotic form of the amplitude 301
§ 13.4. Simplest consequences of the Regge-pole hypothesis. The diffraction peak and the total cross-section 
309 
§ 13.5. Properties of Regge trajectories 317
CHAPTER 14. DUALITY AND THE VENEZIANO MODEL 
325 
§ 14.1. Finite energy sum rules 325
§ 14.2. Duality. Duality diagrams 330
§ 14.3. The Yeneziano model 335
§ 14.4. Some applications of the Veneziano model 338
CHAPTER 15. ELECTROMAGNETIC AND WEAK CURRENTS. CURRENT ALGEBRA 
343 
§ 15.1. Electromagnetic and weak currents 343
§ 15.2. The Gell-Mann algebra of densities and charges. The groupsSU2XSU3 and SU3XSU3 
351 
§ 15.3. Partial coBservation of axial current 354
§ 15.4. Renormalization of the axial vector coupling constant 358
§ 15.5. Asymptotic chiral symmetry and spectral sun mies 361
§ 15.6. Violation of CP invariance 366
APPENDIX 374
REFERENCES 392
INDEX 398
OTHER TITLES IN THE SERIES IN NATURAL PHILOSOPHY 402

Produkt-Details

• Erscheint lt. Verlag: 22.10.2013
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Sozialwissenschaften ► Ethnologie
• Themenwelt: Sozialwissenschaften ► Politik / Verwaltung
• Themenwelt: Sozialwissenschaften ► Soziologie
• ISBN-10: 1-4831-8731-4 / 1483187314
• ISBN-13: 978-1-4831-8731-0 / 9781483187310