I. INTRODUCTION II. BASIC CONCEPTS A. Minkowski space 1. Coordinates in Minkowski space 2. Causal structure 3. Fourier transform 4. Lorentz and Poincaré groups 5. Double coverings of Lorentz and Poincaré groups 6. Complex Lorentz groups B. General concepts of quantum field theory 1. Quantum mechanics 2. Time reversal 3. Relativistic quantum mechanics 4. Haag-Kastler axioms for observable algebras 5. Haag-Kastler axioms for field algebras 6. Global symmetries 7. Neutral quantum fields 8. Wightman axioms for neutral fields 9. Relationship between Haag-Kastler and Wightman axioms 10. Global symmetries in the Wightman formalism 11. Charged fields 12. Wightman axioms for neutral and charged fields 13.

*U*(1) symmetry 14. Charge conjugation 15. Parity invariance 16. Time reversal invariance 17. The CPT theorem 18. The CPT theorem in a

*P*- and

*T*-invariant theory 19.

*N*-point Wightman and Green's functions C. General scattering theory 1. Time ordered exponential 2. Heisenberg picture 3. Time-dependent perturbations 4. Time ordered Green's functions 5. Adiabatic switching and the energy shift 6. Adiabatic switching and Green's functions 7. Adiabatic scattering theory III. NEUTRAL SCALAR BOSONS A. Free neutral scalar bosons 1. Special solutions and Green's functions 2. Space of solutions 3. Classical fields 4. Poisson brackets 5. Smeared fields 6. Lagrangian formalism 7. Stress-energy tensor 8. Diagonalization of the equations of motion 9. Plane waves 10. Positive frequency space 11. Quantization 12. Quantization in terms of smeared fields 13. Quantization in terms of

*C**-algebras 14. Two-point functions B. Neutral scalar bosons with a linear source 1. Classical fields 2. Lagrangian and Hamiltonian formalism 3. Quantization 4. Operator valued source 5. Scattering operator 6. Green's functions 7. Path integral formulation 8. Feynman rules 9. Vacuum energy 10. Problems with the scattering operator 11. Energy shift and scattering theory for a stationary source 12. Travelling source 13. Scattering cross-sections 14. Inclusive cross-section C. Neutral scalar bosons with a mass-like perturbation 1. Classical fields 2. Lagrangian and Hamiltonian formalism 3. Dynamics in the interaction picture 4. Quantization 5. Quantum Hamiltonian 6. Path integral formulation 7. Feynman rules 8. Vacuum energy 9. Pauli-Villars renormalization 10. Renormalization of the vacuum energy 11. Method of dispersion relations 12. Wick rotation 13. Dimensional renormalization 14. Energy shift IV. MASSIVE PHOTONS A. Free massive photons 1. Space of solutions 2. Classical 4-potentials 3. Poisson brackets 4. Smeared 4-potentials 5. Lagrangian formalism and stress-energy tensor 6. Diagonalization of the equations of motion 7. Plane waves 8. Positive frequency space 9. Spin averaging 10. Quantization B. Massive photons with an external 4-current 1. Classical 4-potentials 2. Lagrangian and Hamiltonian formalism 3. Quantization 4. Causal propagators 5. Feynman rules 6. Path integral formulation 7. Energy shift C. Alternative approaches 1. Classical 4-potentials without the Lorentz condition 2. The Lorentz condition 3. Diagonalization of the equations of motion 4. Positive frequency space 5. “First quantize, then reduce” 6. Quantization without reduction on a positive definite Hilbert space 7. The Gupta-Bleuler approach V. MASSLESS PHOTONS A. Free massless photons 1. Space of solutions and the gauge invariance 2. Classical 4-potentials 3. Smeared 4-potentials 4. Lagrangian formalism and the stress-energy tensor 5. Diagonalization of the equations of motion 6. Positive frequency space 7. Spin averaging 8. Quantization 9. Quantization in terms of

*C**-algebras B. Massless photons with an external 4-current 1. Classical fields 2. Lagrangian and Hamiltonian formalism 3. Quantization 4. Causal propagators 5. Path integral formulation 6. The

*m*→ 0 limit 7. Current produced by a travelling particle 8. Energy shift C. Alternative approaches 1. Manifestly Lorentz covariant formalism 2. The Lorentz condition 3. Positive frequency space 4. “First quantize, then reduce” 5. Quantization with a subsidiary condition 6. The Gupta-Bleuler approach VI. CHARGED SCALAR BOSONS A. Free charged scalar bosons 1. Classical fields 2. Smeared fields 3. Lagrangian formalism 4. Classical 4-current 5. Stress-energy tensor 6. Diagonalization of the equations of motion 7. Plane waves 8. Positive and negative frequency subspace 9. Quantization 10. Quantum 4-current 11. Quantization in terms of smeared fields B. Charged scalar bosons in an external 4-potential 1. Classical fields 2. Lagrangian and Hamiltonian formalism 3. Classical discrete symmetries 4. Quantization 5. Quantum Hamiltonian 6. Quantized discrete symmetries 7. 2

*N*-point Green's functions 8. Path integral formulation 9. Feynman rules 10. Vacuum energy 11. Pauli-Villars renormalization 12. Renormalization of the vacuum energy 13. Method of dispersion relations 14. Dimensional renormalization 15. Abstract gauge covariance 16. Ward identities 17. Energy shift VII. DIRAC FERMIONS A. Free Dirac fermions 1. Dirac spinors 2. Special solutions and Green's functions 3. Space of solutions 4. Classical fields 5. Smeared fields 6. Diagonalization of the equations of motion 7. Plane wave functionals 8. Positive and negative frequency subspaces 9. Spin averaging 10. Quantization 11. Quantization in terms of smeared fields 12. Dirac sea quantization 13. Fermionic Hamiltonian formalism 14. Fermionic Lagrangian formalism 15. Classical 4-current 16. Quantum 4-current B. Dirac fermions in an external 4-potential 1. Dirac equation in an external 4-potential 2. Lagrangian and Hamiltonian formalism 3. Classical discrete symmetries 4. Quantization 5. Quantum Hamiltonian 6. Quantized discrete symmetries 7. 2

*N*-point Green's functions 8. Path integral formulation 9. Feynman rules 10. Vacuum energy 11. Pauli-Villars renormalization 12. Method of dispersion relations 13. Dimensional renormalization 14. Energy shift VIII. MAJORANA FERMIONS A. Free Majorana fermions 1. Charge conjugation 2. Space of solutions 3. Smeared fields 4. Plane waves 5. Quantization 6. Quantization in terms of smeared fields B. Majorana fermions with a mass-like perturbation 1. Classical fields 2. Lagrangian and Hamiltonian formalism 3. Quantum fields 4. Path integral formulation 5. Vacuum energy 6. Renormalization of the vacuum energy 7. Pauli-Villars renormalization of the 2nd order term

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