Cover; Contents; 1 Relativistic quantum mechanics; 1 Quantum mechanics and relativity; 2 Relativistic Schrödinger wave mechanics; 2.1 Relativistic Schrödinger equation; 2.2 Klein-Gordon equation; 2.3 Dirac equation; 2.4 The general conflict between locality and energy positivity; 3 Relativistic particle interactions and quantum mechanics; 3.1 Problems of relativistic particle interactions; 3.2 Field interactions and quantum mechanics; 4 Free field equations and quantum mechanics; 5 Particles as field quanta; 6 Appendix: The Dirac equation; 7 Appendix: Canonical field theory

2 Mathematical problems of the perturbative expansion1 Dyson's perturbative expansion; 2 Dyson argument against convergence; 2.1(Omitted) [Sup(4)] model in zero dimensions; 2.2 (Omitted)[Sup(4)] model in 0+1 dimensions; 2.3 (Omitted)[Sup(4)] 4 model in 1+1 and 2+1 dimensions; 3 Haag theorem; non-Fock representations; 3.1 Quantum field interacting with a classical source; 3.2 Bloch-Nordsieck model; the infrared problem; 3.3 Yukawa model; non-perturbative renormalization; 4 Ultraviolet singularities and canonical quantization; 5 Problems of the interaction picture

6 Appendix: Locality and scattering6.1 Locality and asymptotic states; 6.2 Scattering by a long-range potential; 6.3 Adiabatic switching; 6.4 Asymptotic condition; 7 Wick theorem and Feynman diagrams; 7.1 Compton and electron-electron scattering; electron-positron annihilation; 3 Non-perturbative foundations of quantum field theory; 1 Quantum mechanics and relativity; 2 Properties of the vacuum correlation functions; 3 Quantum mechanics from correlation functions; 4 General properties; 4.1 Spectral condition and forward tube analyticity; 4.2 Lorentz covariance and extended analyticity

2 Euclidean invariance and symmetry3 Reflection positivity; 4 Cluster property; 5 Laplace transform condition; 6 From Euclidean to relativistic QFT; 7 Examples; 8 Functional integral representation; 6 Non-perturbative S-matrix; 1 LSZ asymptotic condition in QFT; 2 Haag-Ruelle scattering theory (massive case); 2.1 One-body problem; 2.2 Large time decay of smooth solutions; 2.3 Refined cluster property; 2.4 The asymptotic limit; 2.5 The S-matrix and asymptotic completeness; 3 Buchholz scattering theory (massless particles); 3.1 Huyghens' principle and locality; 3.2 One-body problem