Editing LSZ reduction formula (section)

{{Short description|Connection between correlation functions and the S-matrix}}
{{Quantum field theory|cTopic=Tools}}
In [[quantum field theory]], the '''Lehmann–Symanzik–Zimmermann''' ('''LSZ''') '''reduction formula''' is a method to calculate [[S-matrix|''S''-matrix]] elements (the [[scattering amplitude]]s) from the [[time ordered|time-ordered]] [[correlation function (quantum field theory)|correlation functions]] of a quantum field theory. It is a step of the path that starts from the [[Lagrangian (field theory)|Lagrangian]] of some quantum field theory and leads to prediction of measurable quantities.  It is named after the three German physicists [[Harry Lehmann]], [[Kurt Symanzik]] and [[Wolfhart Zimmermann]].<ref name="LSZ paper"> {{cite journal |last1=Lehmann |first1=H. |last2=Symanzik |first2=K. |last3=Zimmermann |first3=W. |title=Zur Formulierung quantisierter Feldtheorien |journal=Il Nuovo Cimento |date=January 1955 |volume=1 |issue=1 |pages=205–225 |doi=10.1007/BF02731765 |language=de |publisher=Italian Physical Society|bibcode=1955NCimS...1..205L |s2cid=121373082 }} </ref>

Although the LSZ reduction formula cannot handle [[bound state]]s, [[massless particle]]s and [[topological soliton]]s,  it can be generalized to cover bound states, by use of [[composite field]]s which are often nonlocal. Furthermore, the method, or variants thereof, have turned out to be also fruitful in other fields of theoretical physics. For example, in [[statistical physics]] they can be used to get a particularly general formulation of the [[fluctuation-dissipation theorem]].