Friday, February 24, 2006

S-Matrix Theory

Definition: A theory introduced by Werner Heisenberg in 1943 and developed extensively in the 1950s and 1960s to describe strong interactions in terms of their scattering properties. S-matrix theory uses general properties, such as causality in quantum mechanics and the special theory of relativity. The discovery of quantum chromodynamics as the fundamental theory of strong interactions limited the use of S-matrix theory to a convenient way of deriving general results for scattering in quantum field theories. String theory, as a theory for hadrons, originated in attempts to provide a more fundamental basis for S-matrix theory.

Abandoning attempts to sum all the terms in the strong force expansion, they chose to limit themselves to talking about quantities that could be experimentally measured - probabilities of transitions from an incoming set of quantum states to an outgoing one. The work of field theorists like Chew and Gell-Mann showed that the S-Matrix was a relatively straightforward function of the relevant variables and amenable to various mathematical techniques. This made it possible for S-Matrix research to be conducted without reference to the quantum field theories that it had developed from. Chew proposed the bootstrap philosophy: if the S-Matrix was really an infinite set of coupled equations that determined everything about the hadrons, then it had to have a unique solution, even if it couldn't be calculated exactly.

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