Veneziano amplitude

Short description: 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 [math]\displaystyle{ B(x,y) }[/math], the amplitude is given by^[3]

[math]\displaystyle{ S(k_1,k_2,k_3,k_4) = \frac{2i g_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] }[/math]

where [math]\displaystyle{ \alpha' }[/math] is the string constant, [math]\displaystyle{ k_i }[/math] are the tachyon four-vectors, [math]\displaystyle{ g_o }[/math] is the open string theory coupling constant, and [math]\displaystyle{ \alpha(x) = -1-\alpha'x }[/math].

References

↑ Veneziano, G. (1968). "Construction of a crossing-symmetric, Regge-behaved amplitude for linearly rising trajectories". Nuovo Cimento A 57 (1): 190–7. doi:10.1007/BF02824451. Bibcode: 1968NCimA..57..190V. https://cds.cern.ch/record/390478.
↑ 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. 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
↑ Polchinski, J. (1998). "6". String Theory Volume I: An Introduction to the Bosonic String. Cambridge University Press. p. 183. ISBN 978-0143113799.

External links

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

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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. doi:10.1007/BF02824451. Bibcode: 1968NCimA..57..190V. https://cds.cern.ch/record/390478.

[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. 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

[3] Polchinski, J. (1998). "6". String Theory Volume I: An Introduction to the Bosonic String. Cambridge University Press. p. 183. ISBN 978-0143113799.

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Veneziano amplitude

Topic: Physics

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