S-Matrix

The S- matrix or scattering matrix describes the scattering theory of quantum mechanics and quantum field theory the scattering amplitudes. It was introduced by Wheeler and independently in 1943 by Werner Heisenberg in the quantum theory in 1937 by John Archibald Wheeler in nuclear physics.

The amount of the squares of the elements of the S matrix giving the probability of an initial and a final state, the initial state is in the scattering into the final state.

The axiomatic S- matrix theory, a branch of axiomatic quantum field theory, tried key properties of the S- matrix, such as their unitarity, axiomatically capture. An early success of axiomatic considerations is found by Harry Lehmann, Kurt Symanzik and Wolfhart Zimmermann and named after the initials of their surnames LSZ reduction formula. This indicates that the S- matrix of a quantum field theory can be calculated from the time-ordered n-point functions.

In the 1960s, you did not trust the applicability of conventional quantum field theory in the theory of strong interactions. Here was the S- matrix theory as an alternative and was therefore a very active research field, especially in the school of Geoffrey Chew.

The formulation of an S- matrix is ​​only possible, if before and after the spreading process, the existence of non - interacting fields or asymptotic conditions adopted.

Because the infrared problem in quantum electrodynamics and in quantum field theory on curved space-times, the formulation of a Fock space of asymptotic states at very early and late times in general is not possible, research is being conducted for these cases, alternatives to formulate an S- matrix.

Also in conformal quantum field theories, the definition of an S- matrix is impossible, because the definition of asymptotic fields and states is impossible here; distant points can in fact be represented by a dilation in close points.