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:
“Pleasure is necessarily reciprocal; no one feels it who does not at the same time give it. To be pleased, one must please. What pleases you in others, will in general please them in you.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“The man who would change the name of Arkansas is the original, iron-jawed, brass-mouthed, copper-bellied corpse-maker from the wilds of the Ozarks! He is the man they call Sudden Death and General Desolation! Sired by a hurricane, dam’d by an earthquake, half-brother to the cholera, nearly related to the smallpox on his mother’s side!”
—Administration in the State of Arka, U.S. public relief program (1935-1943)
“Surely one of the peculiar habits of circumstances is the way they follow, in their eternal recurrence, a single course. If an event happens once in a life, it may be depended upon to repeat later its general design.”
—Ellen Glasgow (1873–1945)