Summary
Generalizations of dual-resonance models are discussed within the context of the group-theoretical formulation of the theory. Fields irreducible underSL 2,R transformations are introduced, which are closely related to theSL 2,c irreducible ones. Our scheme has a simple factorization property and is convenient to see resonance structures. To satisfy the cyclic symmetry, three types of constructions of vertices are discussed. Gauge properties are also investigated in a model-independent way. It is shown that the Virasoro's general gauge is realized only for fields with theSL 2,R spin 0, −1/2 and −1. In the light of these results, it is concluded that the general gauge and realistic models\(\alpha _\rho (0) = \frac{1}{2}\) are incompatible in additive models.
Riassunto
Si discutono le generalizzazioni dei modelli della risonanza duale nel contesto della formulazione della teoria in base alla teoria dei gruppi. Si introducono campi irriducibili per trasformazioniSL 2,R ; essi sono in stretta relazione con quelli irriducibili perSL 2,C Il nostro schema ha una semplice, proprietà di fattorizzazione ed è conveniente per vedere le strutture delle risonanze. Per soddisfare la simmetria ciclica, si discutono tre tipi di costruzione dei vertici. Si studiano anche le proprietà di gauge in un modo indipendente dal modello. Si mostra che la gauge generale di Virasoro si realizza solo per campi di spinSL 2,R 0, −1/2 e −1. Alla luce di questi risultati si conclude che la gauge generale ed i modelli realistici\(\alpha _\rho (0) = \frac{1}{2}\) sono incompatibili nei modelli additivi.
Резюме
Обсуждаются дуальные резонансные модели в связи с теоретикогрупповой формулировкой теории. Вводятся неприводимые поля относительноSL 2,R преобразований, которые тесно связаны сSL 2,C неприводимыми полями. Наша схема обладает простым свойством факторизации и удобна для рассмотрения резонанснои структуры. Чтобы удовлетворить циклической симметрии, обсуждаются три типа конструкций вершин. Независимым модельным образом исследуются также калибровочные свойства. Показывается, что общая калибровка Вирасоро реализуется только для полейSL 2,R спином 0, −1/2 и −1. В свете этих результатов утверждается, что общая калибровка и реалистичные модели\(\alpha _\rho (0) = \frac{1}{2}\) являются несовместными в аддитивных моделях.
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Based on a thesis submitted to the Department of Physics, University of Tokyo, in partial fulfillment of the requirements for the Ph. D. Degree.
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Matsumoto, H. An attempt at generalizing dual-resonance models. A group-theoretical approach. Nuov Cim A 10, 445–467 (1972). https://doi.org/10.1007/BF02895906
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DOI: https://doi.org/10.1007/BF02895906