Veneziano amplitude

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. The formula is the following:

${\displaystyle {\frac {\Gamma (-1+{\frac {1}{2}}(k_{1}+k_{2})^{2})\Gamma (-1+{\frac {1}{2}}(k_{2}+k_{3})^{2})}{\Gamma (-2+{\frac {1}{2}}((k_{1}+k_{2})^{2}+(k_{2}+k_{3})^{2}))}}}$ .

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
• Crossing (physics)
• Dual resonance model
• History of string theory
• Regge theory

References

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. 737. Springer. pp. 59–118. doi:10.1007/978-3-540-74233-3_4. ISBN 978-3-540-74232-6. arXiv preprint

External links

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