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Concept
S-matrix theory
Résumé
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. In S-matrix theory, the S-matrix relates the infinite past to the infinite future in one step, without being decomposable into intermediate steps corresponding to time-slices.
This program was very influential in the 1960s, because it was a plausible substitute for quantum field theory, which was plagued with the zero interaction phenomenon at strong coupling. Applied to the strong interaction, it led to the development of string theory.
S-matrix theory was largely abandoned by physicists in the 1970s, as quantum chromodynamics was recognized to solve the problems of strong interactions within the framework of field theory. But in the guise of string theory, S-matrix theory is still a popular approach to the problem of quantum gravity.
The S-matrix theory is related to the holographic principle and the AdS/CFT correspondence by a flat space limit. The analog of the S-matrix relations in AdS space is the boundary conformal theory.
The most lasting legacy of the theory is string theory. Other notable achievements are the Froissart bound, and the prediction of the pomeron.
S-matrix theory was proposed as a principle of particle interactions by Werner Heisenberg in 1943, following John Archibald Wheeler's 1937 introduction of the S-matrix.
It was developed heavily by Geoffrey Chew, Steven Frautschi, Stanley Mandelstam, Vladimir Gribov, and Tullio Regge. Some aspects of the theory were promoted by Lev Landau in the Soviet Union, and by Murray Gell-Mann in the United States.
The basic principles are:
Relativity: The S-matrix is a representation of the Poincaré group;
Unitarity: ;
Analyticity: integral relations and singularity conditions.
The basic analyticity principles were also called analyticity of the first kind, and they were never fully enumerated, but they include
Crossing: The amplitudes for antiparticle scattering are the analytic continuation of particle scattering amplitudes.
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