Editing S-matrix (section)

== History ==
The initial elements of ''S''-matrix theory are found in [[Paul Dirac]]'s 1927 paper "Über die Quantenmechanik der Stoßvorgänge".<ref>{{Cite journal |last=Dirac |first=Paul |date=1927-08-01 |title=Über die Quantenmechanik der Stoßvorgänge |url=https://doi.org/10.1007/BF01451660 |journal=Zeitschrift für Physik |language=de |volume=44 |issue=8 |pages=585–595 |doi=10.1007/BF01451660 |bibcode=1927ZPhy...44..585D |issn=0044-3328|url-access=subscription }}</ref><ref>{{Cite journal |last1=Sanyuk |first1=Valerii I. |last2=Sukhanov |first2=Alexander D. |date=2003-09-01 |title=Dirac in 20th century physics: a centenary assessment |url=https://ufn.ru/en/articles/2003/9/c/ |journal=Physics-Uspekhi |language=en |volume=46 |issue=9 |pages=937–956 |doi=10.1070/PU2003v046n09ABEH001165 |issn=1063-7869|url-access=subscription }}</ref> 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".<ref>John Archibald Wheeler, "[http://link.aps.org/abstract/PR/v52/p1107 On the Mathematical Description of Light Nuclei by the Method of Resonating Group Structure]", ''Phys. Rev.'' 52, 1107–1122 (1937).</ref> In this paper Wheeler introduced a ''scattering matrix'' – a unitary matrix of coefficients connecting "the asymptotic behaviour of an arbitrary particular solution [of the integral equations] with that of solutions of a standard form",<ref name = "Mehra">[[Jagdish Mehra]], [[Helmut Rechenberg]], ''The Historical Development of Quantum Theory'' (Pages 990 and 1031) Springer, 2001 {{ISBN|0-387-95086-9}}, {{ISBN|978-0-387-95086-0}}</ref> but did not develop it fully.

In the 1940s, [[Werner Heisenberg]] independently developed and substantiated the idea of the ''S''-matrix. Because of the problematic divergences present in [[quantum field theory]] at that time, Heisenberg was motivated to isolate the ''essential features of the theory'' that would not be affected by future changes as the theory developed. In doing so, he was led to introduce a unitary "characteristic" ''S''-matrix.<ref name = "Mehra"/>

Today, however, exact ''S''-matrix results are important for [[conformal field theory]], [[integrable systems]], and several further areas of quantum field theory and [[string theory]]. ''S''-matrices are not substitutes for a field-theoretic treatment, but rather, complement the end results of such.