Editing Schwinger function (section)

=== Nelson's axioms ===
These axioms were proposed by [[Edward Nelson]].<ref name="Nelson">{{cite journal | first = Edward| last = Nelson| title=Construction of quantum fields from Markoff fields | journal=Journal of Functional Analysis | volume=12 | issue=1 | date=1973-01-01 | issn=0022-1236 | doi=10.1016/0022-1236(73)90091-8 | pages=97–112 | doi-access=free }}</ref> See also their description in the book of Barry Simon.<ref name="Simon">{{cite book|last=Simon|first=Barry|title=The P(phi)_2 Euclidean (quantum) field theory|publisher=Princeton University Press|year=1974|isbn=0-691-08144-1|publication-place=Princeton, New Jersey|page=|oclc=905864308}}</ref> Like in the above axioms by Glimm and Jaffe, one assumes that the field <math> \phi \in D'(\mathbb{R}^d)</math> is a random distribution with a measure <math>d\mu </math>. This measure is sufficiently regular so that the field <math> \phi</math> has regularity of a [[Sobolev space]] of negative derivative order. The crucial feature of these axioms is to consider the field restricted to a surface. One of the axioms is '''Markov property''', which formalizes the intuitive notion that the state of the field inside a closed surface depends only on the state of the field on the surface.