One-Particle Singularities of the S-Matrix in Quantum Field Theory

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Abstract
In the framework of the Haag‐Ruelle collision theory one‐particle singularities are proved to exist in the physical region of any connected scattering amplitude. They occur with the causal propagator (p2 − m2 + iε)−1 in the dominant term and have a residue, which factors into the product of two connected amplitudes for subprocesses. The remainder of the amplitude is infinitely often differentiable in the critical variable. These results rely essentially on short‐range forces and the one‐particle spectrum, but neither depend on analyticity nor on unitarity.