Dual-symmetric theory of hadrons.—I

Дуальная симметричная теория адронов.—I

Summary

A theory of mesons is based on the experimentally observed linear level spacing of hadron excitations. The theory uses a model for the internal structure of mesons consisting of a system of harmonic vibrations. Roughly speaking, a meson is described by the degrees of freedom of a four-dimensional rubber band with a quark pair embedded in it. The theory satisfies relativistic invariance, crossing symmetry and a generalization of duality which we call dual-symmetry. In the approximation of retaining only tree graphs, the scattering amplitudes are given by then-point dual amplitudes recently proposed by Virasoro, Bardakci and Ruegg, Chan and Goebel and Sakita. In the special case,n=4, we reproduce Veneziano’s formula.

Riassunto

Si basa una teoria mesonica sul distanziamento lineare dei livelli osservato sperimentalmente. La teoria usa un modello per la struttura interna dei mesoni consistente di un sistema di vibrazioni armoniche. Parlando in generale, si descrive un mesone con i gradi di libertà di una striscia di gomma a quattro dimensioni che porta incastonata una coppia di quark. La teoria soddisfa l’invariauza relativistica, la simmetria incrociata ed una generalizzazione della dualità che è chiamata simmetria duale. Facendo l’approssimazione di conservare solo tre grafici, si esprimono le ampiezze di scattering con le ampiezze duali conn punti proposte recentemente da Virasoro, Bardakci e Ruegg, da Chan e Goebel e da Sakita. Nel caso specialen=4 si riottiene la formula di Veneziano.

Резюме

Теория мезона основывается на экспериментально наблюдаемом линейном интервале между уровнями для адронных возбуждений. Эта теория использует модель для внутренней структуры мезонов, состоящую из системы гармонических колебаний. Грубо говоря, мезон описывается степенями свободы для четырехмерного «резинового слоя» с внедренной в него парой кварков. Рассматриваемая теория удовлетворяет релятивистской инвариантности, кроссинг-симметрии и обобщению дуальности, которое мы называем дуальной симметрией. В приближении, сохраняющем лишь древовидные графики, вьшисываются амплитуды рассеяния черезn-точечные дуальные амплитуды, недавно предложенные Вирасоро, Вардакчи и Руеггом, Ченом и Гоебелом и Сакита. В частном случаеn=4 мы воспроизводим формулу Венециано.

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References

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Correspondence to L. Susskind.

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Supported in part by A.F.O.S.R. Grant No. 1282-67.

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Susskind, L. Dual-symmetric theory of hadrons.—I. Nuovo Cimento A (1965-1970) 69, 457–496 (1970). https://doi.org/10.1007/BF02726485

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Keywords

  • Coherent State
  • Vertex Operator
  • Dual Graph
  • External Line
  • Cyclic Order