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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 ...
S-matrix theorists sought to understand the strong interaction by using the analytic properties of the scattering matrix to calculate the interactions of bound-states without assuming that there is a point-particle field theory underneath. The S-matrix approach did not provide a local space-time description.
The initial elements of S-matrix theory are found in Paul Dirac's 1927 paper "Über die Quantenmechanik der Stoßvorgänge". [1] [2] The S-matrix was first properly introduced by John Archibald Wheeler in the 1937 paper "On the Mathematical Description of Light Nuclei by the Method of Resonating Group Structure". [3]
The term "bootstrap model" is used for a class of theories that use very general consistency criteria to determine the form of a quantum theory from some assumptions on the spectrum of particles. It is a form of S-matrix theory.
The S-matrix describes the amplitude for a process with an initial state evolving into a final state .If the initial and final states consist of two clusters, with and close to each other but far from the pair and , then the cluster decomposition property requires the S-matrix to factorize
String theory represents an outgrowth of S-matrix theory, [1] a research program begun by Werner Heisenberg in 1943 [2] following John Archibald Wheeler's 1937 introduction of the S-matrix. [3] Many prominent theorists picked up and advocated S-matrix theory, starting in the late 1950s and throughout the 1960s.
Within the canonical formulation of quantum field theory, a Feynman diagram represents a term in the Wick's expansion of the perturbative S-matrix. Alternatively, the path integral formulation of quantum field theory represents the transition amplitude as a weighted sum of all possible histories of the system from the initial to the final state ...
Born, however, had learned matrix algebra from Rosanes, as already noted, but Born had also learned Hilbert's theory of integral equations and quadratic forms for an infinite number of variables as was apparent from a citation by Born of Hilbert's work Grundzüge einer allgemeinen Theorie der Linearen Integralgleichungen published in 1912. [16 ...