Veneziano amplitude

1968 physics-related discovery

In theoretical physics, the Veneziano amplitude refers to the discovery made in 1968 by Italian theoretical physicist Gabriele Veneziano that the Euler beta function, when interpreted as a scattering amplitude, has many of the features needed to explain the physical properties of strongly interacting mesons, such as symmetry and duality.[1] Conformal symmetry was soon discovered. This discovery can be considered the birth of string theory,[2] as the invention of string theory came about as a search for a physical model which would give rise to such a scattering amplitude. In particular, the amplitude appears as the four tachyon scattering amplitude in oriented open bosonic string theory. Using Mandelstam variables and the beta function B ( x , y ) {\displaystyle B(x,y)} , the amplitude is given by[3]

S ( k 1 , k 2 , k 3 , k 4 ) = 2 i g o 2 α ′ ( 2 π ) 26 δ 26 ( Σ i k i ) [ B ( α ( s ) , α ( t ) ) + B ( α ( s ) , α ( u ) ) + B ( α ( t ) , α ( u ) ) ] {\displaystyle S(k_{1},k_{2},k_{3},k_{4})={\frac {2ig_{o}^{2}}{\alpha '}}(2\pi )^{26}\delta ^{26}(\Sigma _{i}k_{i}){\big [}B(\alpha (s),\alpha (t))+B(\alpha (s),\alpha (u))+B(\alpha (t),\alpha (u)){\big ]}}

where  α ′ {\displaystyle \alpha '} is the string constant,  k i {\displaystyle k_{i}} are the tachyon four-vectors,  g o {\displaystyle g_{o}} is the open string theory coupling constant, and  α ( x ) = − 1 − α ′ x {\displaystyle \alpha (x)=-1-\alpha 'x} .

## See also

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* Beta function
* Crossing (physics)
* Dual resonance model
* History of string theory
* Regge theory
* Chan–Paton factor

## References

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1. ^ Veneziano, G. (1968). "Construction of a crossing-symmetric, Regge-behaved amplitude for linearly rising trajectories". Nuovo Cimento A. 57 (1): 190–7\. Bibcode:1968NCimA..57..190V. doi:10.1007/BF02824451.
2. ^ Di Vecchia, P. (2008). "The Birth of String Theory". In Gasperini, Maurizio; Maharana, Jnan (eds.). String Theory and Fundamental Interactions – Gabriele Veneziano and Theoretical Physics: Historical and Contemporary Perspectives. Lecture Notes in Physics. Vol. 737\. Springer. pp. 59–118\. doi:10.1007/978-3-540-74233-3_4. ISBN 978-3-540-74232-6. arXiv preprint
3. ^ Polchinski, J. (1998). "6". String Theory Volume I: An Introduction to the Bosonic String. Cambridge University Press. p. 183\. ISBN 978-0143113799.

## External links

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* String Theory and M-Theory, Lecture 6, Video lecture by Leonard Susskind on Veneziano amplitude. (Stanford University)

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