Editing Schwinger function (section)

{{Short description|Euclidean Wightman distributions}} 
In [[quantum field theory]], the [[Wightman distribution]]s can be [[Analytic continuation|analytically continued]] to analytic functions in [[Euclidean space]] with the [[Domain of a function|domain]] restricted to ordered ''n''-tuples in <math>\mathbb R^d</math> that are pairwise distinct.<ref name="Streater">{{cite book | last1=Streater | first1=R. F. | last2 = Wightman |first2 = A.S.| title=PCT, spin and statistics, and all that | publisher=Princeton University Press | publication-place=Princeton, N.J | year=2000 | isbn=978-0-691-07062-9 | oclc=953694720 | page=}}</ref> These functions are called the '''Schwinger functions''' (named after [[Julian Schwinger]]) and they are real-analytic, symmetric under the permutation of arguments (antisymmetric for [[fermionic field]]s), Euclidean covariant and satisfy a property known as '''reflection positivity'''. Properties of Schwinger functions are known as '''Osterwalder–Schrader axioms''' (named after [[Konrad Osterwalder]] and [[Robert Schrader]]).<ref name=":0">Osterwalder, K., and Schrader, R.: "Axioms for Euclidean Green’s functions," ''Comm. Math. Phys.'' '''31''' (1973), 83–112; '''42''' (1975), 281–305.</ref> Schwinger functions are also referred to as '''Euclidean correlation functions'''.