Quarks, Leptons, and Gauge Fields
(World Scientific, Singapore, 1992) 348 pages
ISBN 981-02-0695-3 981-02-0660-7 (pbk)
To order online go to World Scientific, find book under Physics, High Energy Physics.
FROM THE PREFACE
According to the current view, the basic building blocks of matter are quarks and leptons, which interact with one another through the intermediaries of Yang Mills gauge fields (gravity being ignored in this context). This means that the forms of the interactions are completely determined by the algebraic structure of certain internal symmetry groups. Thus, the strong interactions are associated with the group SU(3), and is described by a gauge theory called quantum chromodynamics. The electro-weak interactions, as described by the now standard Weinberg- Salam model, is associated with the group SU(2) x U(l). This book is a concise introduction to the physical motivation behind these ideas, and precise mathematical formulation thereof. The goal of the book is to explain why and how the mathematical formalism helps us to understand the relevant observed phenomena. The audience for which this book is written are graduate students in physics who have some knowledge of the experimental parts of particle physics, and an acquaintance with quantum field theory, including Feynman graphs and the notion of renormalization.
1 INTRODUCTION Particles and Interactions Gauge Theories of Interactions Notations and Conventions 2 QUARKS Internal Symmetries Representation of SU(3) The Quark Model Color Electromagnetic and Weak Probes Charm 3 MAXWELL FIELD: U(1) GAUGE THEORY Global and Local Gauge Invariance Spontaneous Breaking of Global Gauge Invariance: Goldstone Mode Spontaneous Breaking of Local Gauge Invariance: Higgs Mode Classical Finite-Energy Solutions Magnetic Flux Quantization Soliton Solutions: Vortex Lines 4 YANG-MILLS FIELDS: NON-ABELIAN GAUGE THEORIES Introductory Note Lie Groups The Yang-Mills Constructions Properties of Yang-Mills Fields Canonical Formalism Spontaneous Symmetry Breaking 5 TOPOLOGICAL SOLITONS Solitons The Instanton The Monopole 6 WEINBERG-SALAM MODEL The Matter Fields The Gauge Fields The General Theory 7 METHOD OF PATH INTEGRALS Non-Relativistic Quantum Mechanics Quantum Field Theory External Sources Euclidean 4-Space Calculation of Path Integrals The Feynman Propagator Feynman Graphs Boson Loops and Fermion Loops Fermion Fields 8 QUANTIZATION OF GAUGE FIELDS Canonical Quantization Path Integral Method in Hamiltonian Form Feynman Path Integral: Fadeev-Popov Method Free Maxwell Field Pure Yang-Mills Fields The Theta-World and the Instanton Gribov Ambiguity Projection Operator for Gauss' Law 9 RENORMALIZATION Charge Renormalization Perturbative Renormalization in Quantum Electrodynamics The Renormalization Group Scalar Fields Renormalizability Phi4 theory Triviality" and the Landau ghost The Physics of Renormalization Renormalization of QED 10 METHOD OF EFFECTIVE POTENTIAL Spontaneous Symmetry Breaking The Effective Action The Effective Potential The Loop Expansion One-Loop Effective Potential Renormalization Dimensional Transmutation A Non-Relativistic Example Application to Weinberg-Salam Model 11 THE AXIAL ANOMALY Origin of the Axial Anomaly The Triangle Graph Anomalous Divergence of the Chiral Current Physical Explanation of the Axial Anomaly cancellation of Anomalies 't Hooft's Principle 12 QUANTUM CHROMODYNAMICS General Properties The Color Gyromagnetic Ratio Asymptotic Freedom The Pion as Goldstone Boson The U(1) Puzzle Theta Worlds in QCD 13 LATTICE GAUGE THEORY Wilson's Lattice Action Transfer Matrix Lattice Hamiltonian Lattice Fermions Wilson Loop and Confinement Continuum Limit Monte Carlo Methods 14 QUARK CONFINEMENT Wilson Criterion and Electric Confinement String Model of Hadrons Superconductivity: Magnetic Confinement Electric and Magnetic Order Parameters Scenario for Quark Confinement Symmetry and Confinement