Editing Von Neumann algebra (section)

==Applications==
Von Neumann algebras have found applications in diverse areas of mathematics like [[knot theory]], [[statistical mechanics]], [[quantum field theory]], [[local quantum physics]], [[free probability]], [[noncommutative geometry]], [[representation theory]], [[differential geometry]], and [[dynamical system]]s.

For instance, [[C*-algebra]] provides an alternative axiomatization to probability theory. In this case the method goes by the name of [[Gelfand–Naimark–Segal construction]]. This is analogous to the two approaches to measure and integration, where one has the choice to construct measures of sets first and define integrals later, or construct integrals first and define set measures as integrals of characteristic functions.