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:
“In communist society, where nobody has one exclusive sphere of activity but each can become accomplished in any branch he wishes, society regulates the general production and thus makes it possible for me to do one thing today and another tomorrow, to hunt in the morning, fish in the afternoon, rear cattle in the evening, criticize after dinner, just as I have a mind, without ever becoming hunter, fisherman, shepherd or critic.”
—Karl Marx (1818–1883)
“At Hayes’ General Store, west of the cemetery, hangs an old army rifle, used by a discouraged Civil War veteran to end his earthly troubles. The grocer took the rifle as payment ‘on account.’”
—Administration for the State of Con, U.S. public relief program (1935-1943)
“It has been the struggle between privileged men who have managed to get hold of the levers of power and the people in general with their vague and changing aspirations for equality, for justice, for some kind of gentler brotherhood and peace, which has kept that balance of forces we call our system of government in equilibrium.”
—John Dos Passos (1896–1970)