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Particle Physics and Introduction to Field Theory PDF

876 Pages·1981·29.48 MB·English
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Trim 1/2 in off the top of all covers Front edge of spine-----------8.875in from the front edge of the paper. Trim small here ----- Trim large here --- TF2759 ISBN 3 7186 0033 1 *Small covers trim to (14.625 x 9.4) *Large covers trim to (18.875 x 11.4) Particle Physics ana Introduction to Field Theory Contemporary A series edited by Henry Primakoff, Concepts University of Pennsylvania in Physics Associate Editors: Eli Burstein University of Pennsylvania Willis Lamb University of Arizona Leon Lederman Fermi National Accelerator Laboratory Sir Rudolf Peierls Oxford University Mal Ruderman Columbia University Volume 1 Particle Physics and Introduction to Field Theory Additional volumes in preparation. Science Press (Beijing) Particle Physics ana Introduction to Field Theory T.D. Lee Columbia University CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2004 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20140806 International Standard Book Number-13: 978-1-4822-8719-6 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reason- able efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. 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Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com TO JEANNETTE TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk Contents Preface to the Series . . • . . . . . . . . . . . . . . • . . . . • . . . xv Preface xvii Part I: Introduction to Field Theory Chapter 1: Mechanics of a Finite System {Review) • • • • • • 3 1.1 Classical Mechanics • • • • • • • • • • • • • • • • • • • 3 1. 2 Quantization . . . . . . . . . . . . . . . . . . . . . . • . 4 1.3 Some Genera I Theorems • • • • • • • • • • • • • . • • 10 Chapter 2: The Spin-O Field • • • • • • • • • • • • • • • • .. • • 17 2.1 General Discussion • • • • • • • • . . • • • • . • • • • 17 2.2 Fourier Expansion (Free or Interacting Fields) • • • 20 2.3 Hilbert Space (Free or Interacting Fields) • . • • • 25 Chapter 3 : The Spin-! Field • • • • • • • • • • • • • • • • • • • • 29 3.1 Mathematical Preliminaries • • • . • • • • • • • • • • 29 3.2 Free Field . • • . . . . . . . . . . • • • • • • . • . • . . 31 3.3 Quantization (Free or Interacting Fields) • • • • • 32 3.4 Fourier Expansion {Free or Interacting Fields) • • • 34 3.5 Hilbert Space (Free or Interacting Fields) • • • • • 37 3.6 Momentum and Angular Momentum Operators • • • 41 3.7 Phase Factor Conventions between the Spinors • • 45 3.8 Two-component Theory • . • . • • • • • • • • • • • • • 49 Chapter 4: The Spin-1 Field (m I 0) •••••••.••••• 55 4. 1 Free Field ..........•.......•....•• 55 4.2 I11h~rading Field$ 58 Chapter 5: Feynman Diagrams 62 5.1 Heisenberg, Schr!XIinger and Interaction Representations • 62 5.2 S-Matrix 66 vii. 5.3 Time-ordered Products, Normal Products and Contractions 72 5.4 Perturbation Series •.•••••••.•.•...••• 78 5. 5 Wick Theorem ••••••••••.••.•.••.••• 80 5.6 App I i cations • . • • • • • . . • . • . . . • • • • • • . • 84 5.7 Differential Cross Sections for 1 + 2 - 1' + 2' + ..• + n' 92 Chapter 6 : Quantum Electrodynamics 103 6.1 Lagrangian •••..•••..•••.••••.••••• 103 6.2 Coulomb Gauge ••.•••••....•..•..•• 104 6.3 Quantization •••••.•••.••..••••••.• 107 6.4 Photon Propagator and Relativistic Invariance 109 6.5 Remarks •..•.••••••••••••••..•.••• 113 Chapter 7: Solitons 117 7.1 Early History . . • • • . • . . • • . • . . . . • • • . • 117 7.2 Definition, Classification and Some General Remarks 123 7.3 One-space-dimensional Examples • . • . . • • • • 128 -Topological soliton. Nontopological soliton. 7.4 Derrick Theorem . • • • . • • • • • • • • . • • • . . . 138 7.5 Solitons vs. Plane Waves . • • • . • • . • • . • • • 141 -One space-dimension. Two space-dimensions. Three space-dimensions. 7.6 Quantization • • . • . • • • • • • • • • . • • • . . . • 150 -Lagrangian, Hamiltonian and commutation relations. Coli ecti ve coordinates. Perturbation expansion. Part II : Particle Physics Chapter 8 : Order-of-magnitude Estimations 161 8.1 Radius of the Hydrogen Atom • • • • . . • • • . • 162 8.2 Hadron Size • • . • . . • . . . • • • • • • • . . . • • . 163 8.3 High-energy pp, 1rp and Kp Total Cross Sections 164 8.4 e+ + e- - (J+ + fJ- • • • • • • • • • • • . • • • • • • 165 8.5 v + N - ••· • • • • • • • • • . . • . • • • • . . . • 167 8.6 Compton Scattering • . • • • • . . . . . . • . • . . . 168 8.7 Mass Singularity and High-energy Behavior 170 8.8 e+ e- Pair Production by High-energy Photons 173 viii. Part IIA: Particle Physics: Symmetry Chapter 9 : General Discussion 177 9.1 Non-observables, Symmetry Transformations and Conservation Laws 178 9.2 Asymmetries and Observables • • • . • • • • • • . • 181 u Chapter 10 : 1 Symmetry and P, C Invari once • • • • • 189 10.1 QED as an Example • . . • . . • . • . • • . • • • • 189 10.2 Applications . • • • . . . . • . • . • • . . • • • • • . 199 -Furry theorem. Positronium states. Decay of a f spin-0 particle - 2y. Spin-1 particle 2y. 10.3 General Discussion • • • • . • • • • • • • • • • • . • 208 10.4 Baryon Number and Lepton Number • • . • • • • 210 Chapter 11 Isotopic Spin and G Parity 217 11. 1 lsospi n • • • . • . . • • • • • • • • • • . • • • • • . • • 21 7 -u 2 symmetry. lsospi n transformations. 11.2 G Parity • . . • • • . • • . • . • . • • . • • . . . . • 225 -Nucleon-antinucleon system. The quantum num ber G. 11.3 Applications to Mesons and Baryons • . • . . • • 230 -Pion. Vector mesons. A and kaon. Meson and baryon octets. 11.4 Isospin Violation • • • • . • • • • • • • • • . • • • • • 240 -Electromagnetic interaction. Weak interaction. u Chapter 12 : S 3 Symmetry • • • • • • • . • • • • • • • • • • • 251 12.1 Mathematical Preliminary . • • . • • • • • • • • • 253 -Tensors. Representations. Decomposition of ® ® . x Some further properties. Excur- sion to other groups. 12.2 Hadron States and Their Flavor and Color Symmetries • 265 -Pseudoscalar octet. Baryon spin--! octet and spin·~ decuplet. 12.3 Mass Formulas • • • • • • • • • • • • • . • • • • • . • 273 -Hasym and the spurion formulation. Octet mass formulas. Decuplet mass formula. ix.

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