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:
“Private property is held sacred in all good governments, and particularly in our own. Yet shall the fear of invading it prevent a general from marching his army over a cornfield or burning a house which protects the enemy? A thousand other instances might be cited to show that laws must sometimes be silent when necessity speaks.”
—Andrew Jackson (1767–1845)
“It has been an unchallengeable American doctrine that cranberry sauce, a pink goo with overtones of sugared tomatoes, is a delectable necessity of the Thanksgiving board and that turkey is uneatable without it.... There are some things in every country that you must be born to endure; and another hundred years of general satisfaction with Americans and America could not reconcile this expatriate to cranberry sauce, peanut butter, and drum majorettes.”
—Alistair Cooke (b. 1908)
“To judge from a single conversation, he made the impression of a narrow and very English mind; of one who paid for his rare elevation by general tameness and conformity. Off his own beat, his opinions were of no value.”
—Ralph Waldo Emerson (1803–1882)