General
In quantum field theory, the operator product expansion (OPE) is a convergent expansion of the product of two fields at different points as a sum (possibly infinite) of local fields.
More precisely, if x and y are two different points, and A and B are operator-valued fields, then there is an open neighborhood of y, O such that for all x in O/{y}
where the sum is over finitely or countably many terms, Ci are operator-valued fields, ci are analytic functions over O/{y} and the sum is convergent in the operator topology within O/{y}.
OPEs are most often used in conformal field theory.
The notation is often used to denote that the difference G(x,y)-F(x,y) remains analytic at the points x=y. This is an equivalence relation.
Read more about this topic: Operator Product Expansion
Famous quotes containing the word general:
“‘A thing is called by a certain name because it instantiates a certain universal’ is obviously circular when particularized, but it looks imposing when left in this general form. And it looks imposing in this general form largely because of the inveterate philosophical habit of treating the shadows cast by words and sentences as if they were separately identifiable. Universals, like facts and propositions, are such shadows.”
—David Pears (b. 1921)
“That sort of half sigh, which, accompanied by two or three slight nods of the head, is pity’s small change in general society.”
—Charles Dickens (1812–1870)
“Every writer is necessarily a critic—that is, each sentence is a skeleton accompanied by enormous activity of rejection; and each selection is governed by general principles concerning truth, force, beauty, and so on.... The critic that is in every fabulist is like the iceberg—nine-tenths of him is under water.”
—Thornton Wilder (1897–1975)