Summary
The detailed structure of the two-sided symmetric chain-of-partition-labelled formalism, introduced in the first paper of this series, is systematically investigated for the three-, four- andN-body problem. This allows for a transparent comparison with previous step-by-step approaches, based on analogical or recurrence procedures. Chain elementaryT-operators, related to physical transition amplitudes, are introduced from the very beginning through an explicit definition from which their dynamical equations can be straightforwardly derived. In the framework of our general chain-of-partition-labelled approach, the different aspects and the complexities of theN-body problem, which are differently emphasized in the various existing formulations, can be handled under a unifying perspective.
Riassunto
Si studiano sistematicamente le proprietà delle equazioni aN corpi, simmetriche rispetto agli indici di catene di partizioni, che sono state introdotte nel primo lavoro di questa serie. Si considerano in dettaglio i casi con tre o quattro corpi. Ciò rende agevole il confronto tra la nostra teoria e precedenti formulazioni basate su procedimenti analogici o ricorsivi. Si definiscono esplicitamente sin dall’inizio opportuni operatori, contrassegnati da indici di catena, che permettono di costruire in modo semplice e naturale le ampiezze fisiche di transizione. Le equazioni dinamiche per questi operatori sono derivate direttamente dalla loro stessa definizione e dalle equazioni per i risolventi elementari. Nell’ambito del nostro formalismo generale si possono trattare da un punto di vista unitario i vari complessi aspetti della teoria aN corpi, che sono posti in luce in modo diverso nelle varie formulazioni esistenti del problema aN corpi.
Реэюме
Для случая трех-, четырех- иN-частиц систематически исследуется подробная структура формалиэма, симметричного относительно индексов цепочки распределения, который был введен в первой статье зтой серии. Проводится последовательно сравнение с предыдушими подходами, основанными на аналогичной или рекурентной процедурах. Исходя иэ определения в явном виде, вводятся злементарныеT-операторы цепочки, свяэанные с фиэическими амплитудами переходов. Динамические уравнения для зтих операторов могут быть получены непосредственно иэ того же определения. В рамках нащего обшего подхода можно рассмотреть раэличные сложные аспекты проблемыN-частиц с единой точки эрения.
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Cattapan, G., Vanzani, V. New developments inN-body scattering theory. — II. Nuov Cim A 81, 447–484 (1984). https://doi.org/10.1007/BF02724527
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DOI: https://doi.org/10.1007/BF02724527