Dual resonance model

Dual resonance model

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In theoretical physics
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...

, a dual resonance model arose the early investigation (1968–1974) of string theory as an S-matrix theory
S-matrix theory
S-matrix theory was a proposal for replacing local quantum field theory as the basic principle of elementary particle physics.It avoided the notion of space and time by replacing it with abstract mathematical properties of the S-matrix...

 of the strong interaction
Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...


It was based upon the observation that the amplitudes for the s-channel scatterings matched exactly with the amplitudes for the t-channel scatterings among meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...

s and also the Regge trajectory. It began with the Euler beta function model of Gabriele Veneziano
Gabriele Veneziano
Gabriele Veneziano, born in Florence, Italy), is an Italian theoretical physicist and the founder of string theory. . Has spent most of his scientific activities at CERN in Geneva, Switzerland...

 in 1968 for a 4-particle amplitude
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...

 which has the property that it is explicitly s-t crossing symmetric, exhibits duality between the description in terms of Regge poles or of resonances, and provides a closed-form solution to non-linear finite-energy sum rules relating s- and t- channels.

The Veneziano formula was quickly generalized to an equally consistent N-particle amplitude for which, in chronological order Yoichiro Nambu
Yoichiro Nambu
is a Japanese-born American physicist, currently a professor at the University of Chicago. Known for his contributions to the field of theoretical physics, he was awarded a one-half share of the Nobel Prize in Physics in 2008 for the discovery of the mechanism of spontaneous broken symmetry in...

 (1968), Holger Bech Nielsen
Holger Bech Nielsen
Holger Bech Nielsen is a Danish theoretical physicist, professor at the Niels Bohr Institute, at the University of Copenhagen, where he started studying physics in 1961....

 (1969), and Leonard Susskind
Leonard Susskind
Leonard Susskind is the Felix Bloch Professor of Theoretical Physics at Stanford University. His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology...

 (1969), provided a physical interpretation in terms of an infinite number of simple harmonic oscillators describing the motion of an extended one-dimensional string, whence string theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...


The study of dual resonance models was very popular from 1968 to 1974. It fell rapidly out of favor around 1974 mainly because it was superseded by quantum chromodynamics
Quantum chromodynamics
In theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...

as the accepted theory of strong interactions.