The Past and Future of S-Matrix Theory

Contents: 1. Introduction. 2. The Early Years. 2.1 Living Without Field Theory. 2.2 Initial Postulates. 2.3 Further Postulates. 2.4 QCD and a Final Postulate. 2.5 Analyticity in Field Theory. 3. Axiomatic S-Matrix Theory. 3.1 Unitarity, Bubble Diagrams and Landau Diagrams. 3.2 The Landau Equations and the ``$+~ \alpha$'' Condition. 3.3 Macrocausality and Essential Support. 3.4 The Structure Theorem. 3.5 Local Discontinuity Formulae. 3.6 Good and Bad Functions and the Steinmann Relations. 3.7 Global Discontinuity Formulae. 3.8 CPT, Hermitian Analyticity, etc. 3.9 Holonomy. 4. Asymptotic S-Matrix Theory. 4.1 The Elastic Scattering Asymptotic Dispersion Relation. 4.2 Multiparticle Kinematics and Analyticity Domains. 4.3 Multiparticle Asymptotic Dispersion Relations. 4.4 Classification of Multiple Discontinuities. 5. Multi-Regge Theory. 5.1 Partial-Wave Expansions. 5.2 Froissart-Gribov Continuations. Sommerfeld-Watson Representations. 5.4 Reggeon Unitarity. 6. Reggeon Field Theory. 6.1 Pomeron Phase-Space and the Effective Lagrangian. 6.2 The Critical Pomeron. 6.3 The Super-Critical Pomeron. 7. QCD and the Critical Pomeron. 7.1 Reggeon Diagrams in QCD. 7.2 Color Superconductivity and the Super-Critical Pomeron. 7.3 Quark Saturation and an Infra-Red Fixed Point. 7.4 Uniqueness of the S-Matrix ?