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Strings and beta function.

  1. Feb 23, 2006 #1
    I watched the elegant universe and one scienetist noticed the euler beta function seemed to explain what he was doing and it had properties of a vibrating string.

    So I'm wondering if I could find his original paper, explanation or some additional info.
  2. jcsd
  3. Feb 24, 2006 #2
    The physicist's name is Veneziano if that helps your searching. I'd type something out (it's elaborated on in 'Superstring Theory' by Green, Schwarz and Witten) but I've a lecture.
  4. Feb 24, 2006 #3


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    Also google on "Dual Model", It started out with considering the basic H-shaped Feynmann diagram description of a simple interaction; two particles p-1 and p-2 come in (bottom legs of the H), interact (crossbar of the H) and are transformed into two outgoing particles q_1 and q_2 (top legs of the H). Suppose you repace the crossbar of the H with a cartoon cloud labelled "Then an interaction happens". Physicists in the 1960 pointed out the experimental data can't really "see" the interaction and it's unprofessional to assume as much as the crossbar suggests. In fact you can't really distinguish the decription I just gave from the one where p_1 and q_1 come in from the left, interact, and become p_2 and q_2 exiting to the right. It was asserted that physics should be symmetric with respect to this dual explanation; neither "channel" should be preferred.

    Veneziano then found that the symmetric mathematical model was defined by the beta function. In fact if you call the first description the s-channel and the second one the t-channel (traditional names) and they have individual amplitudes s and t, then the amplitude for the four particle interaction, as given by Veneziano, is

    [tex] g^2 B(-\frac{s}{2} -2, -\frac{t}{2}-2)[/tex]

    Where g is the coupling strength. (From GSW Superstring Theory, Vol 1, Page 50). And this can be shown to describe the amplitude of a quantized vibrating string.
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