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:
“What journeyings on foot and on horseback through the wilderness, to preach the gospel to these minks and muskrats! who first, no doubt, listened with their red ears out of a natural hospitality and courtesy, and afterward from curiosity or even interest, till at length there “were praying Indians,” and, as the General Court wrote to Cromwell, the “work is brought to this perfection that some of the Indians themselves can pray and prophesy in a comfortable manner.””
—Henry David Thoreau (1817–1862)
“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)
“A constitutional statesman is in general a man of common opinions and uncommon abilities.”
—Walter Bagehot (1826–1877)