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Twisting-invariant factorization of multiparticle dual amplitude

Факторизация, инвариантная относительно кручения, для многочастичной дуальной амплитуды

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Il Nuovo Cimento A (1965-1970)

Summary

We exhibit a transformation of variables which allows the simultaneous factorization of a multiparticle Veneziano term and its twisted counterpart (obtained by reversing the order of the intial or final particles). The states which factorize the amplitude are linear combinations of those previously obtained which were not invariant under twisting. The behaviour of the couplings under twisting allows the definition of a signature factor. The invariance under double twist is automatically satisfied. It is shown that the properties under the aforementioned transformation lead to relations between the couplings of the states to scalar particles (some of them are the ones called «Ward identities» in the literature).

Riassunto

Mediante una trasformazione di variabili dell'ampiezza di Veneziano per processi multipli, riusciamo a fattorizzare simultaneamente un qualsiasi termine di questa ampiezza e quello ottenuto da esso invertendo l'ordine delle particelle iniziali o finali («twist»). Gli stati che fattorizzano l'ampiezza in questo modo— e che sono combinazioni lineari di quelli ottenuti precedentemente nella letteratura—posseggono una firma («signature») definita. L'invarianza per doppio «twist» risulta essere automatica Le proprietà di trasformazione dell'ampiezza per i cambiamenti di variabili su indicati generano delle relazioni (chiamate «identità di Ward» nella letteratura) tragli accoppiamenti di questi stati a particelle scalari esterne.

Резюме

Мы показываем преобразование переменных, которое допускает одновременную факторизацию многочастичного члена Венециано и его крученого двойника (полученного путем переворачивания порядка начальных или конечных частиц). Состояния, которые факторизуют амплитуду, являются линейными комбинациями предварительно полученных состояний, которые не являются инвариантными относительно кручения. Поведение постоянных связи при кручении позволяет определить сигнатурный множитель. Инвариантность при двойном кручении автоматически вьшолняется. Показывается, что свойства при вышеупомянутом преобразовании приводят к соотношениям между постоянными связи этих состояний со скалярными частицами (некоторые из них называются в литературе «тождествами Уорда»).

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References

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  8. Notice that ourV (n)'s differ from those of Fubini and Veneziano by a normalization factor 2n. Furthermore, we use the metricg 00=−g ii=+1, and take all momenta ingoing.

  9. There may be some regularity conditions ofF at the points ϱi=0 and 1; (2.5) is certainly true ifF is regular at these points, and this is all what we need in what follows. It is easily seen that we can also allow poles of finite order. Furthermore, we can relax the bootstrap conditions (3) α(μ2)=0 and give arbitrary masses to the

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Authors and Affiliations

  1. CERN, Geneva

    D. Amati, M. Le Bellac & D. Olive

  2. Physique Théorique, Nice

    M. Le Bellac

  3. DAMTP, Cambridge

    D. Olive

  4. Churchill College, Cambridge

    D. Olive

Authors
  1. D. Amati
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  2. M. Le Bellac
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  3. D. Olive
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Amati, D., Le Bellac, M. & Olive, D. Twisting-invariant factorization of multiparticle dual amplitude. Nuovo Cimento A (1965-1970) 66, 815–830 (1970). https://doi.org/10.1007/BF02824723

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  • DOI: https://doi.org/10.1007/BF02824723

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