Summary
The partial-wave integral equations connecting the three-particle amplitudes are derived from the Fadeev equations written in a form due to Lovelace. The kernel of these equations is studied by operator techniques to derive analyticity properties in the total energys and in a particular continuation of the total angular momentumJ (viz., that in which the relative angular momentum between any pair of particles is kept fixed). It is found that the amplitudes are meromorphic in the product of theJ ands planes except for kinematical cuts in theJ-plane and the three-particle and bound-state scattering cuts in thes-plane.
Riassunto
Dalle equazioni di Fadeev, scritte in una forma dovuta a Lovelace, si deducono le equazioni integrali dell’onda parziale che connettono le ampiezze di tre particelle. Si studia il nocciolo di queste equazioni con tecniche di operatori per dedurre le proprietà di analiticità nell’energia totales ed in una particolare continuazione del momento angolare totaleJ (cioè, quella in cui il momento angolare relativo fra ciascuna coppia di particelle è mantenuto fissato). Si trova che le ampiezze sono meromorfiche nel prodotto dei pioniJ eds eccetto per tagli cinematici nel pianoJ e per i tagli dello scattering di tre particelle e dello stato legato nel pianos.
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References
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An erratum to this article is available at http://dx.doi.org/10.1007/BF02734855.
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Choudhury, M.H. Complex angular momentum and energy in three-particle amplitudes. Nuovo Cim 34, 956–980 (1964). https://doi.org/10.1007/BF02812524
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DOI: https://doi.org/10.1007/BF02812524