Summary
A set of twelve coupled equations gives the four-particle transition operator. The kernel involves three- and two-particle transi-tion operators only and not convolutions of two-particle transition operators as in other treatments. The four-particle transition operator satisfies two-particle unitarity in each two-particle channel. An extension of the concept of a four-particle resolvent operator is given which may simplify the many-body equations.
Riassunto
Un gruppo di dodici equazioni accoppiate dà l’operatore di transizione di quattro par-ticelle. II nocciolo coinvolge solo operatori di transizione di tre e due particelle e non convoluzioni di operatori di transizione di due particelle come in altri trattamenti. L’operatore di transizione di quattro particelle soddisfa l’unitarietà di due particelle in ogni canale di due particelle. Si espone un'estensione del concetto di operatore risolvente di quattro pnrticelle che può semplificare il problema di molti corpi.
Резюме
Система двенадцати связанных уравнений определяет оператор четырех-частичного перехода. Ядро нключает только операторы трех-частичиьх и двух-частичиых переходов и не сод⪂ржит сверток операторов двух-частичных переходов, как при других рассмотрениях. Оператор четырех-частичного перехода у↓овлетворяет двух-частичной унитарности в каждом двух-частином канале. При-водится обобшение концепции оператора четырех-частичной резольвенты, которое может упростить много-частичные уравненеия.
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Riordan, F. Four-Particle Faddeev Equations with a Simple Kernel.. Nuov Cim A 3, 53–81 (1971). https://doi.org/10.1007/BF02912610
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DOI: https://doi.org/10.1007/BF02912610