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:
“We will win this war because we are willing to sacrifice 10,000,000 lives. How many lives is the White Man willing to sacrifice?”
—Jerome Cady, U.S. screenwriter, and Lewis Milestone. General Mitsubi (Richard Loo)
“In effect, to follow, not to force the public inclination; to give a direction, a form, a technical dress, and a specific sanction, to the general sense of the community, is the true end of legislature.”
—Edmund Burke (1729–1797)
“Towards him they bend
With awful reverence prone; and as a God
Extoll him equal to the highest in Heav’n:
Nor fail’d they to express how much they prais’d,
That for the general safety he despis’d
His own: for neither do the Spirits damn’d
Loose all thir vertue; lest bad men should boast
Thir specious deeds on earth, which glory excites,
Or close ambition varnisht o’er with zeal.”
—John Milton (1608–1674)