Summary
The scattering formalism for the multiparticle systems interacting before and after scattering—in particular for unstable particles, resonances and clusters—is outlined. The main formal tool proposed here is an auxiliary pre-asymptotic spaceH =H in =H out deseribing the self-interacting «ingoing» and «outgoing» multiparticle states. The characteristic features of the states in ℋ—continuous mass spectra and virtual propagation—are briefly discussed. We show further that the physical unitarity condition is satisfied and double counting avoided if in the auxiliary space ℋ the phase space is properly defined.
Riassunto
Si delinea il formalismo dello scattering per i sistemi di molte particelle che interagiscono prima e dopo lo scattering — in particolare per particelle instabili, risonanze ed ammassi. Il principale strumento formale che qui si propone è uno spazio ausiliario preasintoticoH =H in =H out che descrive gli stati autointeragenti di molte particelle «entranti» e «uscenti». Si discutono in breve i lineamenti caratteristici degli stati inH—spettri continui di massa e propagazione virtuale. Si fa vedere poi come sia soddisfatta la condizione fisica di unitarietà e si eviti il doppio conteggio se si definisce propriamente lo spazio delle fasi nello spazio ausiliarioH.
Реэюме
Описывается формалиэм рассеяния для многочастичных систем, вэаимодействуюших до и после рассеяния, в частности для нестабильных частиц, реэо-нансов и кластера. Основной формальный инструмент, предложенный в работе, представляет вспомогательное предасимптотическое пространство Ж = Жin=Жout, описываюшее «падаюшее» и «рассеянное» многочастичные состояния с собственным вэаимодействием. Вкратце обсуждаются основные характеристики состояний в Ж-o непрерывные массовые спектры и виртуальный пропагатор. Затем мы покаэываем, что удовлетворяется фиэическое условие унитарности и не воэникает двойной подсчет, если в вспомогательном пространстве Ж надлежашим обраэом определяется фаэовое пространство.
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Lukierski, J. On the scattering formalism for interacting multiparticle subsystems. Nuov Cim A 23, 716–732 (1974). https://doi.org/10.1007/BF02821987
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DOI: https://doi.org/10.1007/BF02821987