Summary
An analogy is drawn between the real photons appearing in electrodynamics and the photonlike particle appearing in the dual-resonance model with unit intercept. Sum rules for the Compton scattering of these particles are derived and, by employing the analogy, interpreted in terms of low-energy theorems. In particular we rederive the «universal» property of magnetic moments and the lack of anomalous moments in the dual model. We also show that the Beg-type sum rule exists and is saturated by relatively few states. This is a direct result of the simplicity of the collinear algebra appearing in the dual model.
Riassunto
Si traccia un'analogia fra i fotoni reali che compaiono nell'elettrodinamica e la particella simile al fotone che compare nel modello della risonanza duale con intercetta unitaria. Si deducono le regole di somma per lo scattering Compton di queste particelle e, facendo uso dell'analogia, le si interpreta in termini dei teoremi di bassa energia. In particolare si deduce nuovamente la proprietà «universale» dei momenti magnetici e la mancanza di momenti anomali nel modello duale. Si dimostra anche che la regola di somma del tipo di Beg esiste ed è saturata da relativamente pochi stati. Ciò risulta direttamente dalla semplicità dell'algebra collineare che compare nel modello duale.
Резюме
Устанавливается аналогия между реальными фотонами, появляющимися в электродинамике и частицей, подобной фотону, появляющейся в дуальной резонансной модели с единичным пересечением. Выводятся правила сумм для комптоновского рассеяния таких частиц, которые с помощью полученной аналогии интерпретируются в терминах теорем низких энергий. В частности, мы заново выводим «универсаляное» свойство магнитных моментов и отсытствие наомальных моментов в дуальной модели. Мы также показываем, что существует правило сумм беговского типа, которое насыщается сравнителяно небольщим числом состояний. Это представляет непосредственное проявление простоты коллинеарной алгебры, появляущейся в дуальной модели.
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References
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This work was supported in part through funds provided by the Atomic Energy Commission under Contract AT (11-1)-3069 and NSF grant No. GP 30819X.
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Friedman, K.A., Rosenzweig, C. Photonlike particles, Compton scattering and sum rules in the dual-resonance model. Nuov Cim A 10, 53–60 (1972). https://doi.org/10.1007/BF02895973
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DOI: https://doi.org/10.1007/BF02895973