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. 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 $B(x,y)$ , the amplitude is given by^[3]

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 $\alpha '$ is the string constant, $k_{i}$ are the tachyon four-vectors, $g_{o}$ is the open string theory coupling constant, and $\alpha (x)=-1-\alpha 'x$ .

References edit

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

External links edit

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. 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.

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Veneziano amplitude

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