Veneziano amplitude

In theoretical physics, the Veneziano amplitude refers to the discovery made in 1968 by Italian theoretical physicist Gabriele Veneziano that the Euler gamma 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. The formula is the following:

$\frac{ \Gamma (-1+\frac12(k_1+k_2)^2) \Gamma (-1+\frac12(k_2+k_3)^2) } { \Gamma (-2+\frac12((k_1+k_2)^2+(k_2+k_3)^2)) }$ .

k_n is a vector (such as a four-vector) referring to the momentum of the n^th particle. Γ is the gamma function.

This discovery can be considered the birth of string theory,^[2] as the discovery and invention of string theory came about as a search for a physical model which would give rise to such a scattering amplitude.

See also

• Beta function
• Dual resonance model

External links

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

References

1. Veneziano, G. (1968). "Construction of a crossing-symmetric, Regge-behaved amplitude for linearly rising trajectories". Nuovo Cimento A 57: 190–7.
2. Di Vecchia, P. (2008). "The Birth of String Theory". In Gasperini, Maurizio; Maharana, Jnan. String Theory and Fundamental Interactions – Gabriele Veneziano and Theoretical Physics: Historical and Contemporary Perspectives (PDF). Lecture Notes in Physics 737. Springer. pp. 59–118. ISBN 978-3-540-74232-6.