Viewing the OPE as a relation between correlation functions shows that the OPE must be associative. Furthermore, if the space is Euclidean, the OPE must be commutative, because correlation functions do not depend on the order of the fields, i.e. O 1 ( x 1 ) O 2 ( x 2 ) = O 2 ( x 2 ) O 1 ( x 1 ) .