Abstract
Previous proofs of asymptotic completeness and related results on scattering in field theories are restricted toP(ϕ)2 models in the 2- and 3-particle regions. In this paper, new cluster expansions that are well adapted to more direct proofs and generalizations of these results are presented. In contrast to previous ones, they are designed to provide direct graphical definitions of general irreducible kernels satisfying structure equations recently proposed and shown to be closely linked with asymptotic completeness and with the multiparticle structure of Green functions and collision amplitudes in general energy regions. The method can be applied as previously toP(ϕ)2 and can also be extended to theories involving renormalization which are controlled by phase-space analysis. It is here illustrated in detail for the Bethe-Salpeter kernel in ϕ 42 , in which case a new proof of its 4-particle decay (which yields asymptotic completeness in the 2-particle region) is given.
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Communicated by K. Osterwalder
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Iagolnitzer, D., Magnen, J. Asymptotic completeness and multiparticle structure in field theories. Commun.Math. Phys. 110, 51–74 (1987). https://doi.org/10.1007/BF01209016
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DOI: https://doi.org/10.1007/BF01209016