Abstract
By analyzing the Bethe-Salpeter equation for even λ℘(φ)2 models we show that for weak coupling the mass spectrum is discrete and of finite multiplicity below 2m. Moreover on even states of energy less than 4(m−ɛ) we show that theS matrix is unitary. Herem is the physical mass and ɛ=ɛ(λ)→0 as λ→0. Our results rely essentially only on a simple assumption about the analyticity of the Bethe-Salpeter kernel which has been verified for weak coupling. For the interaction λφ4, (λ/m 2o ≪1) we show that there are no even bound states of energy less than 4(m−ɛ).
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Communicated by A.S. Wightman
Work supported in part by NSF, Grant MPS 74-13252
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Spencer, T., Zirilli, F. Scattering states and bound states in λ℘(φ)2 . Commun.Math. Phys. 49, 1–16 (1976). https://doi.org/10.1007/BF01608631
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DOI: https://doi.org/10.1007/BF01608631