Advanced Quantum Theory

For the past five years, my editor at Springer-Verlag has asked me to write a second edition of this text that would incorporate new material on the quark model. Because this is a subject at the forefront of modern physics, whose central ideas are perpetually in flux, such an addition is not a simple task. Nevertheless, I have tried to discuss quark model topics that should stand the test of time and be of interest to introductory advanced quantum mechanics students as examples of the Feynman diagram technique. I have also tried to eliminate errors made in the first edition. I appreciate the work of R. Miller, who graciously typed the additional material. My colleagues V. Elias, T. Hakioglu, S. Kocic, N. Paver, and R. Thews helped me formulate the quark model chapter. Tucson, Arizona M. D. Scadron May 1990 vii Preface to the First Edition The fundamental goal of physics is an understanding of the forces of nature in their simplest and most general terms. Yet the scientific method inadver­ tently steers us away from that course by requiring an ever finer subdivision of the problem into constituent components, so that the overall objective is often obscured, even to the experts. The situation is most frustrating and acute for today's graduate students, who must try to absorb as much general knowledge as is possible and also try to digest only a small fraction of the ever increasing morass of observational data or detailed theories to write a dissertation.

Contenu

I Transformation Theory.- 1 Introduction.- 1.A Principles of Quantum Mechanics.- 1.B Angular-Momentum Expansions.- 1.C Unitary Operators and Transformation Theory.- 1.D Translations in Time.- 2 Transformations in Space.- 2.A Continuous Symmetry Transformations and Group Theory.- 2.B Translations in Space.- 2.C Rotations in Space.- 2.D The Rotation Group O(3).- 2.E Tensor Operators and the Wigner-Eckart Theorem.- 3 Transformations in Space-Time.- 3.A Lorentz Velocity Transformations.- 3.B Homogeneous Lorentz Group L.- 3.C Inhomogeneous Lorentz Group P.- 3.D Helicity Formalism.- 4 Boson Wave Equations.- 4.A Spin-0 Klein-Gordon Equation.- 4.B Spin-1 Wave Equation.- 4.C Spin-1 Maxwell Equation.- 4.D Second Quantization: Photons and Phonons.- 5 Spin-$$\frac{1}{2}$$ Dirac Equation.- 5.A Derivations of the Dirac Equation.- 5.B Covariant Formulation.- 5.C Free-Particle Solutions of the Dirac Equation.- 5.D Dirac Equation in an External Field.- 5.E Wave Equations for Other Fermi Particles.- 6 Discrete Symmetries.- 6.A Charge-Conjugation Transformation.- 6.B Space-Reflection Transformations.- 6.C Time-Reversal Transformation.- 6.D CPT Invariance.- II Scattering Theory.- 7 Formal Theory of Scattering.- 7.A Formulation of the Scattering Problem.- 7.B Time-Independent Potential Scattering.- 7.C Time-Dependent Scattering in the Schrödinger Picture.- 7.D Time-Dependent Scattering in the Interaction Picture.- 7.E The S-Matrix.- 7.F Transition Probabilities.- 7.G Unitarity and Probability Conservation.- 7.H Bound States in Scattering Language.- 8 Simple Scattering Dynamics.- 8.A Partial Waves and Phase Shifts.- 8.B Low-Energy Scattering and Bound States.- 8.C Resonance Scattering, Formation, and Decay.- 8.D Born Approximation in Potential Scattering.- 8.E Form Factors.- 8.F High-Energy Scattering.- 9 Nonrelativistic Perturbation Theory.- 9.A Time-Independent Perturbation Theory.- 9.B Time-Dependent Perturbation Theory.- 9.C Electron-Photon Interactions in Atoms.- 9.D Electron-Phonon Interactions in Solids.- Ill Covariant Feynman Diagrams.- 10 Covariant Feynman Rules.- 10.A Covariant Kinematics.- 10.B Covariant S-Matrix.- 10.C Covariant Vertices.- 10.D Covariant Feynman Propagators.- 10.E Feynman Rules in Momentum Space.- 11 Lowest-Order Electromagnetic Interactions.- 11.A Coulomb Scattering.- 11.B Moller Scattering.- 11.C Bhabha Scattering.- 11.D Compton Scattering.- 11.E Bremsstrahlung and Pair Production.- 11.F Electromagnetic Interactions of Hadrons.- 11.G Static Electromagnetic Potentials.- 12 Low-Energy Strong Interactions.- 12.A Yukawa Force.- 12.B Isospin.- 12.C One-Pion-Exchange Nucleon-Nucleon Force.- 12.D Low-Energy ?N Scattering.- 12.E Hadronic Vector Currents.- 12.F Hadronic Axial-Vector Currents.- 13 Lowest-Order Weak Interactions.- 13.A Phenomenology of Weak Decays.- 13.B Current-Current Hypothesis.- 13.C Muon Decay.- 13.D Neutron ?-Decay.- 13.E Charged-Pion Decay.- 13.F Cabibbo Universality.- 13.G Nonleptonic Decays.- 14 Lowest-Order Gravitational Interactions.- 14.A Graviton Wave Function and Propagator.- 14.B Graviton Vertices.- 14.C Graviton Spontaneous Emission.- 14.D Quantum Corrections to the Newtonian Force Law.- 14.E Gravitational Light Bending.- 14.F Connection between Quantum Theory of Gravity and General Relativity.- 15 Higher-Order Covariant Feynman Diagrams.- 15.A Closed-Loop Diagrams.- 15.B Electron Anomalous Magnetic Moment.- 15.C Self-Energy Loop Diagrams.- 15.D Free-Electron Charge Form Factor.- 15.E Bound-State Lamb Shift.- 15.F Renormalization in Field Theory.- 15.G Dispersion Theory and QED.- 15.H Dispersion Theory and Strong Interactions.- 16 Quark Model at Low Energies.- 16.A Flavor, Spin, and Color Symmetry of Quarks.- 16.B Magnetic Moments and Mass Formulae.- 16.C Chiral Symmetry and Nambu-Goldstone Pions.- 16.D Chiral Symmetry and Quark Loops.- 16.E Linear ? Model to One-Loop Order.- Problems.- Appendices.- I Units and Conventions.- 1. Units.- 2. Metric and ?-Matrices.- 3. Normalizations.- 4. Decay Rates and Cross Sections.- 5. Covariant Integrals and Feynman Parametrization.- II Rotation-Group Formulae.- III Elementary-Particle Zoo.- Books.- Research Articles.