In this post, we will see the book *Introduction To Elementary Particle Theory* by Yu. V. Novozhilov.

# About the book

The present book is meant as an introduction to such a constructive theory of elementary particles. The author hopes that such a book will be useful as a complement to other texts on elementary particle theory.

The book consists of four parts. The introductory Part I acquaints the reader with the basic description of elementary particles. In Part II questions of relativistic quantum mechanics and kinematics are set forth; Part III is devoted to the problem of internal symmetry, and Part IV to those new dynamical approaches which are likely to have the greatest influence on the development of theory in the future. Quantum electrodynamics and renormalization are excluded from the present book, as these questions are contained in the standard quantum theory of fields. The author does not give a systematic review of experimental data, but cites only the information essential to illustrate the pattern of phenomena and to connect theory with experiment. The Appendix contains tables of particles, but the reader’s main reference on particle properties should be special annual reviews.

The list of references contains only those works which, in the author’s opinion, are basic. The reader may acquaint himself with a more complete list in books and in reviews referred to here. The plan of the book essentially follows the program of courses on elementary particle theory given in the Physics Faculty of Leningrad University.

The reader must be familiar with nonrelativistic quantum mechanics and classical relativity theory. It would also be very useful to have a preliminary acquaintance with the fundamentals of the Lagrangian formulation of quantum field theory and with Feynman diagrams. A course in elementary particle field theory usually is preceded by a short course on group theory. We thus assume that the basic facts of group theory are known to the reader.

The book was translated from Russian by Jonathan Rosner was published in 1975.

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You can get the book here.

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# Contents

Preface ix

Author’s Preface to The English Edition xi

Translator’s Preface xii

Nomenclature xiii

## Chapter 1 Elements of Relativistic Quantum Theory 3

§ 1.1 Homogeneity of space-time and the Poincaré group 4

§ 1.2 Quantum Mechanics and Relativity 7

§ 1.3 Basic Quantities 14

## Chapter 2 Foundations of Phenomenological Description 24

§ 2.1 Interactions and Internal Symmetry 25

§ 2.2 Symmetry and Particle Classification 29

§ 2.3 Unstable Particles 31

## Chapter 3 The Lorentz Group and The Group SL(2,c) 41

§ 3.1 Second-order unimodular matrices and the Lorentz Transformation 41

§ 3.2 Spinors 46

§ 3.3 Irreducible representations and generalized spinor analysis 50

§ 3.4 Direct products of representations and covariant Clebsch-Gordon coefficients 55

§ 3.5 Representation of the unitary group SU_{2}

## Chapter 4 The Quantum Mechanical Poincaré Group 60

§ 4.1 Introductory Remarks 60

§ 4.2 Transformation and Momenta. The little group and Wigner operator 62

§ 4.3 Unitary representations. Case m^2 > 0 67

§ 4.4 Spinor functions and quantum fields for m^{2} > 0 73

§ 4.5 Unitary representations in the case m = 0. Equations of motion. 79

## Chapter 5 Wave Functions and Equations of Motion for Particles with Arbitrary Spin 90

§ 5.1 Wave functions, bilinear Hermitian forms, and equations of motion 91

§ 5.2 The Dirac Equation 94

§ 5.3 2(2J+1)-component functions of spin 105

§ 5.4 Particles with spin J = 1 107

§ 5.5 Rarita-Schwinger Wave Functions 109

§ 5.6 Bargman-Schwinger Wave Functions 113

§ 5.7 The Duffin-Kemmer Equation 116

## Chapter 6 Reflections 118

§ 6.1 Total Reflection 𝜃, or CPT 119

§ 6.2 Operations P, C, and T 129

§ 6.3 Reflections and Interactions. Decay 136

§ 6.4 Summary of Formulae for Reflection Transformation 142

## Chapter 7 Scattering Matrix Kinematics 146

§ 7.1 The problem of kinematics 146

§ 7.2 The variables s, t, and u 148

§ 7.3 Cross sections for processes. Unitarity and optical theorem 153

§ 7.4 Helicity amplitudes 158

§ 7.5 Spinor amplitudes (ℳ-functions) and invariant amplitudes 162

## Chapter 8 Isospin Symmetry 175

§ 8.1 Isospin multiplets, hypercharge and the group SU_{2} 175

§ 8.2 Isospins and reflections. Antiparticle states. G-parity 179

§ 8.3 Multiparticle states and isospin amplitudes. Decays and relations between reactions 184

## Chapter 9 The Group SU_{3} 190

§ 9.1 The Matrices 𝝀_{a} and structure constants 190

§ 9.2 The fundamental representation and quarks. U- and V- spin. 193

§ 9.3 Representations of Group SU_{3} 196

## Chapter 10 SU_{3} Symmetry and the Classification of Particles and Resonances 204

§ 10.1 Unitary Representations and Multiplets 204

§ 10.2 Symmetry breaking and mass splitting 212

§ 10.3 Relations between transition amplitudes 215

§ 10.4 The Quark Model 219

## Chapter 11 The S-Matrix, Current, And Crossing Symmetry 229

§ 11.1 Interpolating fields, currents, and the reduction formula 229

§ 11.2 Crossing symmetry 235

§ 11.3 Crossing matrices for SU_{2} and SU_{3} 240

§ 11.4 Properties of vertex parts 242

## Chapter 12 Analytic Properties of The Scattering Amplitude 247

§ 12.1 Unitarity and absorptive part 247

§ 12.2 Maximal Analyticity 254

§ 12.3 Dispersion Relations 257

§ 12.4 Partial Wave amplitude and fixed energy dispersion relations. The Gribov-Froissart Formular 263

§ 12.5 Analytic properties of form factors. The pion form factor 270

## Chapter 13 Asymptotic Behavior of the Scattering Amplitude at High Energies. Regge Poles 277

§ 13.1 Scattering at High Energies (experiment) 277

§ 13.2 Bounds on amplitudes at high energies 281

§ 13.3 The Regge-pole hypothesis and the asymptotic form of the amplitude 286

§ 13.4 Simplest consequences of Regge-pole hypothesis. The diffraction peak and total cross section 294

§ 13.5 Properties of Regge Trajectories 302

## Chapter 14 Duality and Veneziano Model 310

§ 14.1 Finite Energy Sum Rules 310

§ 14.2 Duality. Duality diagrams 315

§ 14.3 The Veneziano Model 320

§ 14.4 Some applications of the Veneziano model 323

## Chapter 15 Electromagnetic and Weak Currents. Current Algebra 328

§ 15.1 Electromagnetic and weak currents 328

§ 15.2 The Gell-Mann algebra of densities and charges. The groups SU_{2} × SU_{2} and SU_{3} × SU_{3} 336

§ 15.3 Partial Conservation of Axial Current 339

§ 15.4 Renormalization of the axial vector coupling constant 343

§ 15.5 Asymptotic chiral symmetry and spectral sum rules 346

§ 15.6 Violation of CP invariance 351

Appendix 359

References 375

Index 381