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Advanced Quantum Theory : And Its Applications Through Feynman Diagrams : Theoretical and Mathematical Physics - Michael D. Scadron

Advanced Quantum Theory : And Its Applications Through Feynman Diagrams

Theoretical and Mathematical Physics


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The goal of this textbook is to understand the forces of nature in their simplest and most general terms. It begins in Part 1 with a detailed discussion of transformation theory, which is used by the author to formulate advanced quantum theory in group-theoretical language. Part 2 deals with scattering theory and includes many applications to nuclear, atomic, and solid-state physics. The central theme of the book, however, is presented in Part 3: relativistic Feynman diagrams. The student learns to use them in a most natural way and will find a thorough discussion of the lowest-order electromagnetic, strong, weak, and gravitational interactions. The last chapter deals with the finite parts of higher-order graphs in field theory and dispersion theory. In the second edition errors have been eliminated and the text has been enhanced with the inclusion of new sections on the quark model.

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 Schrodinger 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.

ISBN: 9783540536819
ISBN-10: 3540536817
Series: Theoretical and Mathematical Physics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 410
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 2.24
Weight (kg): 0.6
Edition Number: 2
Edition Type: Revised