Summary
We study the problem of the hadron mass spectrum starting from anS-matrix which is explicitly considered as a unitary operator. Making use of the additional property that the connected partT c is a compact operator, we discuss the approximation ofT c by resonances. The connection with statistics is made by using the Bernstein-Dashen-Ma formalism together with a bootstrap assumption. Although our approach remains open, it allows a critical discussion of subtle issues concerning both the Hagedorn and the dual theories.
Riassunto
Si studia il problema dello spettro di massa adronico, prendendo come punto di partenza una matriceS che è esplicitamente trattata come un operatore unitario. Usando la proprietà addizionale che la parte connessa della matriceS T c è un operatore compatto, si discute l’approssimazione di tale parte connessa mediante risonanze. Il legame con la statistica è ottenuto seguendo il formalismo di Bernstein-Dashen-Ma ed introducendo un’ipotesi di « bootstrap ». Benché il nostro approccio al problema rimanga aperto, esso permette un esame critico di questioni sottili riguardanti sia il modello di Hagedorn che il modello duale.
Реэуме
Мы исследуем проблему массового спектра адронов, исходя иэS матрицы, которая явно рассматривается как унитарныи оператор. Исполяэуя допол-нителяное своиство, что свяэанная частяT c представляет компактныи оператор, мы обсуздаем приблизение дляT c череэ реэонансы. Свяэя со статистикои полу-чается эа счет исполяэования форзалиэма Бернщтеина-Дащена-Ма вместе с пред-полозением бутстрепа. Хотя нащ подход остается неэамкнутым, он поэволяет провести критическое обсуздение соответствууших реэулятатов, относяшихся как к теории Хагедорна, так и к дуалянои теории.
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Address after 1 November 1972
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Bassetto, A., Sertorio, L. Critical questions concerning a statistical approach to the hadron mass spectrum. Nuov Cim A 14, 548–566 (1973). https://doi.org/10.1007/BF02756274
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DOI: https://doi.org/10.1007/BF02756274