Gauge Theories in Particle Physics, 40th Anniversary Edition : A Practical Introduction, Volume 1 : From Relativistic Quantum Mechanics to QED, Fifth Edition

The fifth edition of this well-established, highly regarded two-volume set continues to provide a fundamental introduction to advanced particle physics while incorporating substantial new experimental results, especially in the areas of Higgs and top sector physics, as well as CP violation and neutrino oscillations. It offers an accessible and practical introduction to the three gauge theories comprising the Standard Model of particle physics: quantum electrodynamics (QED), quantum chromodynamics (QCD), and the Glashow-Salam-Weinberg (GSW) electroweak theory.Volume 1 of this updated edition provides a broad introduction to the first of these theories, QED. The book begins with self-contained presentations of relativistic quantum mechanics and electromagnetism as a gauge theory. Lorentz transformations, discrete symmetries, and Majorana fermions are covered. A unique feature is the elementary introduction to quantum field theory, leading in easy stages to covariant perturbation theory and Feynman graphs, thereby establishing a firm foundation for the formal and conceptual framework upon which the subsequent development of the three quantum gauge field theories of the Standard Model is based. Detailed tree-level calculations of physical processes in QED are presented, followed by an elementary treatment of one-loop renormalization of a model scalar field theory, and then by the realistic case of QED. The text includes updates on nucleon structure functions and the status of QED, in particular the precision tests provided by the anomalous magnetic moments of the electron and muon.The authors discuss the main conceptual points of the theory, detail many practical calculations of physical quantities from first principles, and compare these quantitative predictions with experimental results, helping readers improve both their calculation skills and physical insight.Each volume should serve as a valuable handbook for students and researchers in advanced particle physics looking for an introduction to the Standard Model of particle physics. Cover Half Title Title Page Copyright Page Dedication Contents Preface I. Introductory Survey, Electromagnetism as a Gauge Theory, and Relativistic Quantum Mechanics 1. The Particles and Forces of the Standard Model 1.1. Introduction: the Standard Model 1.2. The fermions of the Standard Model 1.2.1. Leptons 1.2.2. Quarks 1.3. Particle Interactions in the Standard Model 1.3.1. Classical and quantum fields 1.3.2. The Yukawa theory of force as virtual quantum exchange 1.3.3. The one-quantum exchange amplitude 1.3.4. Electromagnetic interactions 1.3.5. Weak interactions 1.3.6. Strong interactions 1.3.7. The gauge bosons of the Standard Model 1.4. Renormalization and the Higgs sector of the Standard Model 1.4.1. Renormalization 1.4.2. The Higgs boson of the Standard Model 1.5. Summary Problems 2. Electromagnetism as a Gauge Theory 2.1. Introduction 2.2. The Maxwell equations: current conservation 2.3. The Maxwell equations: Lorentz covariance and gauge invariance 2.4. Gauge invariance (and covariance) in quantum mechanics 2.5. The argument reversed: the gauge principle 2.6. Comments on the gauge principle in electromagnetism Problems 3. Relativistic Quantum Mechanics 3.1. The Klein–Gordon equation 3.1.1. Solutions in coordinate space 3.1.2. Probability current for the KG equation 3.2. The Dirac equation 3.2.1. Free-particle solutions 3.2.2. Probability current for the Dirac equation 3.3. Spin 3.4. The negative-energy solutions 3.4.1. Positive-energy spinors 3.4.2. Negative-energy spinors 3.4.3. Dirac’s interpretation of the negative-energy solutions of the Dirac equation 3.4.4. Feynman’s interpretation of the negative-energy solutions of the KG and Dirac equations 3.5. Inclusion of electromagnetic interactions via the gauge principle: the Dirac prediction of g = 2 for the electron Problems 4. Lorentz Transformations and Discrete Symmetries 4.1. Lorentz transformations 4.1.1. The KG equation 4.1.2. The Dirac equation 4.2. Discrete transformations: P, C, and T 4.2.1. Parity 4.2.2. Charge conjugation 4.2.3. CP 4.2.4. Time reversal 4.2.5. CPT Problems II. Introduction to Quantum Field Theory 5. Quantum Field Theory I: The Free Scalar Field 5.1. The quantum field: (i) descriptive 5.2. The quantum field: (ii) Lagrange–Hamilton formulation 5.2.1. The action principle: Lagrangian particle mechanics 5.2.2. Quantum particle mechanics `a la Heisenberg–Lagrange–Hamilton 5.2.3. Interlude: the quantum oscillator 5.2.4. Lagrange–Hamilton classical field mechanics 5.2.5. Heisenberg–Lagrange–Hamilton quantum field mechanics 5.3. Generalizations: four dimensions, relativity, and mass Problems 6. Quantum Field Theory II: Interacting Scalar Fields 6.1. Interactions in quantum field theory: qualitative introduction 6.2. Perturbation theory for interacting fields: the Dyson expansion of the S-matrix 6.2.1. The interaction picture 6.2.2. The S-matrix and the Dyson expansion 6.3. Applications to the ‘ABC’ theory 6.3.1. The decay C → A + B 6.3.2. A + B → A + B scattering: the amplitudes 6.3.3. A + B → A + B scattering: the Yukawa exchange mechanism, s and u channel processes 6.3.4. A + B → A + B scattering: the differential cross section 6.3.5. A + B →A + B scattering: loose ends Problems 7. Quantum Field Theory III: Complex Scalar Fields, Dirac and Maxwell Fields; Introduction of Electromagnetic Interactions 7.1. The complex scalar field: global U(1) phase invariance, particles and antiparticles 7.2. The Dirac field and the spin-statistics connection 7.3. The Maxwell field Aμ(x) 7.3.1. The classical field case 7.3.2. Quantizing Aμ(x) 7.4. Introduction of electromagnetic interactions 7.5. P, C, and T in Quantum field theory 7.5.1. Parity 7.5.2. Charge conjugation 7.5.3. Time reversal Problems III. Tree-Level Applications in QED 8. Elementary Processes 8.1. Coulomb scattering of charged spin-0 particles 8.1.1. Coulomb scattering of s+ (wavefunction approach) 8.1.2. Coulomb scattering of s+ (field-theoretic approach) 8.1.3. Coulomb scattering of s− 8.2. Coulomb scattering of charged spin-1/2 particles 8.2.1. Coulomb scattering of e− (wavefunction approach) 8.2.2. Coulomb scattering of e−(field-theoretic approach) 8.2.3. Trace techniques for spin summations 8.2.4. Coulomb scattering of e+ 8.3. e−s+ scattering 8.3.1. The amplitude for e−s+ → e−s+ 8.3.2. The cross section for e−s+ → e−s+ 8.4. Scattering from a non-point-like object: the pion form factor in e−π+ → e−π+ 8.4.1. e− scattering from a charge distribution 8.4.2. Lorentz invariance 8.4.3. Current conservation 8.5. The form factor in the time-like region: e+e− → π+π− and crossing symmetry 8.6. Electron Compton scattering 8.6.1. The lowest-order amplitudes 8.6.2. Gauge invariance 8.6.3. The Compton cross section 8.7. Electron muon elastic scattering 8.8. Electron–proton elastic scattering and nucleon form factors 8.8.1. Lorentz invariance 8.8.2. Current conservation Problems 9. Deep Inelastic Electron–Nucleon Scattering 9.1. Inelastic electron–proton scattering: kinematics and structure functions 9.2. Bjorken scaling and the parton model 9.3. Partons as quarks and gluons 9.4. The Drell–Yan process 9.5. e+e− annihilation into hadrons Problems IV. Loops and Renormalization 10. Loops and Renormalization I: The ABC Theory 10.1. The propagator correction in ABC theory 10.1.1. The O(g2) self-energy Π[2]C (q2) 10.1.2. Mass shift 10.1.3. Field strength renormalization 10.2. The vertex correction 10.3. Dealing with the bad news: a simple example 10.3.1. Evaluating Π[2]C(q2) 10.3.2. Regularization and renormalization 10.4. Bare and renormalized perturbation theory 10.4.1. Reorganizing perturbation theory 10.4.2. The O(g2ph) renormalized self-energy revisited: how counter terms are determined by renormalization conditions 10.5. Renormalizability Problems 11. Loops and Renormalization II: QED 11.1. Counter terms 11.2. The O(e2) fermion self-energy 11.3. The O(e2) photon self-energy 11.4. The O(e2) renormalized photon self-energy 11.5. The physics of ̄Π[2]γ(q2) 11.5.1. Modified Coulomb’s law 11.5.2. Radiatively induced charge form factor 11.5.3. The running coupling constant 11.5.4. ̄Π[2]γ in the s-channel 11.6. The O(e2) vertex correction, and Z1 = Z2 11.7. The lepton anomalous magnetic moments and tests of QED 11.8. Which theories are renormalizable—and does it matter? Problems V. Appendix A. Non-Relativistic Quantum Mechanics B. Natural Units C. Maxwell’s Equations: Choice of Units D. Special Relativity: Invariance and Covariance E. Dirac δ-function F. Contour Integration G. Green Functions H. Elements of Non-Relativistic Scattering Theory H.1. Time-independent formulation and differential cross section H.2. Expression for the scattering amplitude: Born approximation H.3. Time-dependent approach I. The Schrödinger and Heisenberg Pictures J. Dirac Algebra and Trace Identities J.1. Dirac algebra J.1.1. γ matrices J.1.2. γ5 identities J.1.3. Hermitian conjugate of spinor matrix elements J.1.4. Spin sums and projection operators J.2. Trace theorems K. Example of a Cross Section Calculation K.1. The spin-averaged squared matrix element K.2. Evaluation of two-body Lorentz-invariant phase space in ‘laboratory’ variables L. Feynman Rules for Tree Graphs in QED L.1. External particles L.2. Propagators L.3. Vertices Bibliography Index The fifth edition of this well-established, highly regarded two-volume set continues to provide a fundamental introduction to advanced particle physics while incorporating substantial new experimental results, especially in the areas of Higgs and top sector physics, as well as CP violation and neutrino oscillations. It offers an accessible and practical introduction to the three gauge theories comprising the Standard Model of particle quantum electrodynamics (QED), quantum chromodynamics (QCD), and the Glashow-Salam-Weinberg (GSW) electroweak theory. Volume 1 of this updated edition provides a broad introduction to the first of these theories, QED. The book begins with self-contained presentations of relativistic quantum mechanics and electromagnetism as a gauge theory. Lorentz transformations, discrete symmetries, and Majorana fermions are covered. A unique feature is the elementary introduction to quantum field theory, leading in easy stages to covariant perturbation theory and Feynman graphs, thereby establishing a firm foundation for the formal and conceptual framework upon which the subsequent development of the three quantum gauge field theories of the Standard Model is based. Detailed tree-level calculations of physical processes in QED are presented, followed by an elementary treatment of one-loop renormalization of a model scalar field theory, and then by the realistic case of QED. The text includes updates on nucleon structure functions and the status of QED, in particular the precision tests provided by the anomalous magnetic moments of the electron and muon. The authors discuss the main conceptual points of the theory, detail many practical calculations of physical quantities from first principles, and compare these quantitative predictions with experimental results, helping readers improve both their calculation skills and physical insight. Each volume should serve as a valuable handbook for students and researchers in advanced particle physics looking for an introduction to the Standard Model of particle physics. Ian J.R. Aitchison is Emeritus Professor of Physics at the University of Oxford. He has previously held research positions at Brookhaven National Laboratory, Saclay, and the University of Cambridge. He was a visiting professor at the University of Rochester and the University of Washington, and a scientific associate at CERN and SLAC. Dr. Aitchison has published over 90 scientific papers mainly on hadronic physics and quantum field theory. He is the author of two books and joint editor of further two. Anthony J.G. Hey is now Honorary Senior Data Scientist at the UKs National Laboratory at Harwell. He began his career with a doctorate in particle physics from the University of Oxford. After a career in particle physics that included a professorship at the University of Southampton and research positions at Caltech, MIT and CERN, he moved to Computer Science and founded a parallel computing research group. The group were one of the pioneers of distributed memory message-passing computers and helped establish the MPI message passing standard. After leaving Southampton in 2001 he was director of the UKs eScience initiative before becoming a Vice-President in Microsoft Research. He returned to the UK in 2015 as Chief Data Scientist at the U.K.s Rutherford Appleton Laboratory. He then founded a new Scientific Machine Learning group to apply AI technologies to the Big Scientific Data generated by the Diamond Synchrotron, the ISIS neutron source, and the Central Laser Facility that are located on the Harwell campus. He is the author of over 100 scientific papers on physics and computing and editor of The Feynman Lectures on Computation. The fifth edition of this well-established, highly regarded two-volume set continues to provide a fundamental introduction to advanced particle physics while incorporating substantial new experimental results, especially in the areas of Higgs and top sector physics, as well as CP violation and neutrino oscillations. It offers an accessible and practical introduction to the three gauge theories comprising the Standard Model of particle quantum electrodynamics (QED), quantum chromodynamics (QCD), and the Glashow-Salam-Weinberg (GSW) electroweak theory. New to the fifth Tests of the Standard Model in the Higgs and top quark sectors The naturalness problem and responses to it going beyond the Standard Model The Standard Model as an effective field theory Each volume should serve as a valuable handbook for students and researchers in advanced particle physics looking for an accessible introduction to the Standard Model of particle physics. Anthony J.G. Hey is now Honorary Senior Data Scientist at the UKs National Laboratory at Harwell. He began his career with a doctorate in particle physics from the University of Oxford. After a career in particle physics that included a professorship at the University of Southampton and research positions at Caltech, MIT and CERN, he moved to Computer Science and founded a parallel computing research group. The group were one of the pioneers of distributed memory message-passing computers and helped establish the MPI message passing standard. After leaving Southampton in 2001 he was director of the UKs eScience initiative before becoming a Vice-President in Microsoft Research. He returned to the UK in 2015 as Chief Data Scientist at the U.K.s Rutherford Appleton Laboratory. He then founded a new Scientific Machine Learning group to apply AI technologies to the Big Scientific Data generated by the Diamond Synchrotron, the ISIS neutron source, and the Central Laser Facility that are located on the Harwell campus. He is the author of over 100 scientific papers on physics and computing and editor of The Feynman Lectures on Computation. The fifth edition of this well-established, highly regarded two-volume set continues to provide a fundamental introduction to advanced particle physics while incorporating substantial new experimental results, especially in the areas of Higgs and top sector physics, as well as CP violation and neutrino oscillations. It offers an accessible and practical introduction to the three gauge theories comprising the Standard Model of particle physics: quantum electrodynamics (QED), quantum chromodynamics (QCD), and the Glashow-Salam-Weinberg (GSW) electroweak theory.Volume 2 of this updated edition covers the two non-Abelian gauge theories of QCD and the GSW theory. A distinctive feature is the extended treatment of two crucial theoretical tools: spontaneous symmetry breaking and the renormalization group. The underlying physics of these is elucidated by parallel discussions of examples from condensed matter systems: superfluidity and superconductivity, and critical phenomena. This new edition includes updates to jet algorithms, lattice field theory, CP violation and the CKM matrix, and neutrino physics.New to the fifth edition: Tests of the Standard Model in the Higgs and top quark sectors The naturalness problem and responses to it going beyond the Standard Model The Standard Model as an effective field theory Each volume should serve as a valuable handbook for students and researchers in advanced particle physics looking for an accessible introduction to the Standard Model of particle physics.