List of Exercises
1. Relativistic Description of Spin-O Particles
1.1 Klein-Gordon Equation
1.1.1 Canonical and Lorentz-covariant Formulations of the Klein-Gordon Equation
1.1.2 Hamilton Formulation of the Klein-Gordon Equation
1.1.3 Interpretation of Negative Solutions.Antiparticles
Exercises
1.2 Symmetry Transformations
1.2.1 Active and Passive Transformations
1.2.2 Lorentz Transformations
1.2.3 Discrēte Transformations
Exercises
1.3 One-Particle Interpretation of the Klein-Gordon Theory
1.3.1 Generalized Scalar Product
1.3.2 One-particle Operators
and Feshbach.Villars Representation
1.3.3 Validity Range of the One-particle Concept
1.3.4 Klein Paradox.
Exercises
1.4 Nonrelativistic Approximation of the Klein-Gordon Theory
1.4.1 Nonrelativistic Limit
1.4.2 Relativistic Corrections
Exercises
1.5 Simple One-Particle Systems
1.5.1 Potential Well
1.5.2 Radial Klein-Gordon Equation
1.5.3 Free Particle and Spherically Symmetric Potential Well
1.5.4 Coulomb Potential
1.5.5 Oscillator-Coulomb Potential
Exercises
2. Relativistic Description of Spin-1／2 Particles
2.1 Dirac Equation
2.1.1 Canonical Formulation of the Dirac Equation
2.1.2 Dirac Equation in Lorentz-Covariant Form
2.1.3 Properties of γ-Matrices and Covariant Bilinear Forms
2.1.4 Spin Operator
2.1.5 Projection Operators
2.1.6 Interpretation of Negative Solutions, Antiparticles and Hole Theory
Exercises
2.2 Symmetry Transformations
2.2.1 Proper Lorentz Transformations
2.2.2 Spin of Dirac Solutions
2.2.3 Discrete Transformations
Exercises
2.3 One-Particle Interpretation of the Dirac Theory
2.3.1 One-Particle Operators and Feshbach-Villars Representation
2.3.2 Validity Range of the One-Particle Concept
2.3.3 Klein Paradox
Exercises
2.4 Nonrelativistic Approximation of the Dirac Theory
2.4.1 Nonrelativistic Limit
2.4.2 Relativistic Corrections
Exercises
2.5 Simple One-Particle Systems
2.5.1 Potential Well
2.5.2 Radial Form of the Dirac Equation
2.5.3 Free Particle and Centrally Symmetric Potential Well
2.5.4 Coulomb Potential
Exercises
3. Relativistic Scattering Theory
3.1 Review：Nonrelativistic Scattering Theory
3.1.1 Solution of the General Schr?dinger Equation
3.1.2 Propagator Decomposition by Schr?dinger Solutions
3.1.3 Scattering Formalism
3.1.4 Coulomb Scattering.
Exercises
3.2 Scattering of Spin-1／2 Particles
3.2.1 Solution of the General Dirac Equation
3.2.2 Fourier Decomposition of the Free Fermion Propagator
3.2.3 Scattering Formalism
3.2.4 Trace Evaluations with-γ-Matrices
Exercises
3.3 Spin-1／2 Scattering Processes
3.3.1 Coulomb Scattering of Electrons
3.3.2 Electron-Proton Scattering（Ⅰ）
3.3.3 Electron-Proton Scattering（Ⅱ）
3.3.4 Preliminary Feynman Rules in Momentum Space
3.3.5 Electron-Electron Scattering
3.3.6 Electron-Positron Scattering
3.3.7 Compton Scattering against Electrons
3.3.8 Electron-Positron Annihilation
3.3.9 Conclusion：Feynman Diagrams in Momentum Space
Exercises
3.4 Higher Order Corrections
3.4.1 Vacuum Polarization
3.4.2 Self-Energy
3.4.3 Vortex Correction
3.4.4 Physical Consequences
Exercises.
3.5 Scattering of Spin-O Particles.
3.5.1 Solution of the General Klein-Gordon Equation
3.5.2 Scattering Formalism
3.5.3 Coulomb Scattering of Pions
3.5.4 Pion-Pion Scattering
3.5.5 Pion Production via Electrons
3.5.6 Compton Scattering against Pions
3.5.7 Conclusion：Enhanced Feynman Rules in Momentum Space
Exercises
A.Appendlx
A.1 Theory of Special Relativity
A.2 Bessel Functions, Spherical Bessel Functions
A.3 Legendre Functions，Legendre Polynomials, Spherical Harmonics.
A.4 Dirac Matrices and Bispinors
Index
