A Theory of Scattering for Quasifree Particles

1. Introduction. 1.1. Introduction -- 2. Haag-Kastler fields. 2.1. The Poincare group. 2.2. The Segal *-algebra. 2.3. The Haag-Kastler axioms -- 3. Representations of the Poincare group. 3.1. Induced representations of groups. 3.2. Wigner's theory of symmetry. 3.3. Time-reversal -- 4. The Maxwell field. 4.1. The classical electromagnetic field. 4.2. The C*-norm for electromagnetism -- 5. Some theory of representations. 5.1. The tensor product and Fock space. 5.2. Segal's form of the Weyl relations. 5.3. Representations with coherent states. 5.4. The Segal-Bargmann transform -- 6. Euclidean electrodynamics. 6.1. Some probability theory. 6.2. Markov processes. 6.3. Independence. 6.4. Markov processes with stationary distributions. 6.5. Linear processes. 6.6. Random distributions. 6.7. Fock space and its real-wave realisation. 6.8. Second quantisation. 6.9. The free Euclidean field of spin zero. 6.10. The Nelson axioms. 6.11. Reconstruction of the Hamiltonian from Nelson's axioms -- 7. Models. 7.1. A model in 1 + 1 dimensions. 7.2. Instantons, magnetic poles and solitons. 7.3. An attempt in 1 + 3 dimensions. 7.4. Flat connections. 7.5. Pair production from photon-photon scattering. 7.6. Non-Abelian gauge fields -- 8. Conclusion