Translation group and particle representations in quantum field theory

Description

I. The Axioms of the Theory of Local Observables. 1. The Assumptions of the Theory. 2. Examples: Free Bose Fields. 3. Examples: Free Fermi Fields -- II. Translations and Spectrum Condition. 1. Relations Between Support Properties of Functions and Analytic Properties of Their Fourier Transforms. 2. Symmetry Groups and Continuity. 3. Spaces of Momentum Transfer. 4. Spectrum Condition: The One-Dimensional Case. 5. Characterization of Positive Energy States. 6. The Spectrum in a Cone -- III. The Opposite Edge of the Wedge Problem. 1. Holomorphic Functions of Several Complex Variables. 2. The Edge of the Wedge Theorem. 3. The Double Cone Theorem. 4. The Jost-Lehmann-Dyson Representation. 5. Some Consequences of the Jost-Lehmann-Dyson Representation. 6. Applications: A Hole in the Spectrum -- IV. Locality Condition and the Spectrum of Translations. 1. Commutators and the Edge of the Wedge Problem. 2. Locality and Minimal Translations. 3. Locality and the Shape of the Spectrum