Preface	6
	Table of Contents	11
	List of Exercises	14
	1. Relativistic Description of Spin-0 Particles	16
	1.1 Klein-Gordon Equation	19
	1.1.1 Canonical and Lorentz-covariant Formulationsof the Klein-Gordon Equation	19
	1.1.2 Hamilton Formulation of the Klein-Gordon Equation	24
	1.1.3 Interpretation of Negative Solutions, Antiparticles	27
	Exercises	33
	1.2 Symmetry Transformations	36
	1.2.1 Active and Passive Transformations	36
	1.2.2 Lorentz Transformations	38
	1.2.3 Discrete Transformations	39
	Exercises	44
	1.3 One-Particle Interpretation of the Klein-Gordon Theory	45
	1.3.1 Generalized Scalar Product	45
	1.3.2 One-particle Operatorsand Feshbach-Villars Representation	48
	1.3.3 Validity Range of the One-particle Concept	54
	1.3.4 Klein Paradox	57
	Exercises	61
	1.4 Nonrelativistic Approximation of the Klein-Gordon Theory	66
	1.4.1 Nonrelativistic Limit	66
	1.4.2 Relativistic Corrections	68
	Exercises	73
	1.5 Simple One-Particle Systems	76
	1.5.1 Potential Well	77
	1.5.2 Radial Klein-Gordon Equation	81
	1.5.3 Free Particle and Spherically Symmetric Potential Well	83
	1.5.4 Coulomb Potential	88
	1.5.5 Oscillator-Coulomb Potential	92
	Exercises	97
	2. Relativistic Description of Spin-1/2 Particles	100
	2.1 Dirac Equation	101
	2.1.1 Canonical Formulation of the Dirac Equation	101
	2.1.2 Dirac Equation in Lorentz-Covariant Form	108
	2.1.3 Properties of -Matrices and Covariant Bilinear Forms	112
	2.1.4 Spin Operator	115
	2.1.5 Projection Operators	118
	2.1.6 Interpretation of Negative Solutions, Antiparticlesand Hole Theory	121
	Exercises	128
	2.2 Symmetry Transformations	136
	2.2.1 Proper Lorentz Transformations	136
	2.2.2 Spin of Dirac Solutions	141
	2.2.3 Discrete Transformations	142
	Exercises	148
	2.3 One-Particle Interpretation of the Dirac Theory	152
	2.3.1 One-Particle Operatorsand Feshbach-Villars Representation	152
	2.3.2 Validity Range of the One-Particle Concept	156
	2.3.3 Klein Paradox	158
	Exercises	160
	2.4 Nonrelativistic Approximation of the Dirac Theory	166
	2.4.1 Nonrelativistic Limit	166
	2.4.2 Relativistic Corrections	168
	Exercises	173
	2.5 Simple One-Particle Systems	175
	2.5.1 Potential Well	175
	2.5.2 Radial Form of the Dirac Equation	178
	2.5.3 Free Particle and Centrally Symmetric Potential Well	181
	2.5.4 Coulomb Potential	184
	Exercises	190
	3. Relativistic Scattering Theory	192
	3.1 Review: Nonrelativistic Scattering Theory	193
	3.1.1 Solution of the General Schrödinger Equation	194
	3.1.2 Propagator Decomposition by Schrödinger Solutions	198
	3.1.3 Scattering Formalism	200
	3.1.4 Coulomb Scattering	208
	Exercises	211
	3.2 Scattering of Spin-1/2 Particles	217
	3.2.1 Solution of the General Dirac Equation	218
	3.2.2 Fourier Decomposition of the Free Fermion Propagator	221
	3.2.3 Scattering Formalism	225
	3.2.4 Trace Evaluations with -Matrices	230
	Exercises	235
	3.3 Spin-1/2 Scattering Processes	237
	3.3.1 Coulomb Scattering of Electrons	239
	3.3.2 Electron-Proton Scattering (I)	247
	3.3.3 Electron-Proton Scattering (II)	259
	3.3.4 Preliminary Feynman Rules in Momentum Space	267
	3.3.5 Electron-Electron Scattering	270
	3.3.6 Electron-Positron Scattering	276
	3.3.7 Compton Scattering against Electrons	281
	3.3.8 Electron-Positron Annihilation	289
	3.3.9 Conclusion: Feynman Diagrams in Momentum Space	294
	Exercises	298
	3.4 Higher Order Corrections	307
	3.4.1 Vacuum Polarization	310
	3.4.2 Self-Energy	316
	3.4.3 Vortex Correction	321
	3.4.4 Physical Consequences	325
	Exercises	332
	3.5 Scattering of Spin-0 Particles	334
	3.5.1 Solution of the General Klein-Gordon Equation	334
	3.5.2 Scattering Formalism	336
	3.5.3 Coulomb Scattering of Pions	339
	3.5.4 Pion-Pion Scattering	342
	3.5.5 Pion Production via Electrons	346
	3.5.6 Compton Scattering against Pions	351
	3.5.7 Conclusion: Enhanced Feynman Rulesin Momentum Space	356
	Exercises	358
	A. Appendix	364
	A.1 Theory of Special Relativity	364
	A.2 Bessel Functions, Spherical Bessel Functions	370
	A.3 Legendre Functions, Legendre Polynomials,Spherical Harmonics	372
	A.4 Dirac Matrices and Bispinors	374
	Index	377