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:
“The general review of the past tends to satisfy me with my political life. No man, I suppose, ever came up to his ideal. The first half [of] my political life was first to resist the increase of slavery and secondly to destroy it.... The second half of my political life has been to rebuild, and to get rid of the despotic and corrupting tendencies and the animosities of the war, and other legacies of slavery.”
—Rutherford Birchard Hayes (1822–1893)
“Anti-Nebraska, Know-Nothings, and general disgust with the powers that be, have carried this county [Hamilton County, Ohio] by between seven and eight thousand majority! How people do hate Catholics, and what a happiness it was to show it in what seemed a lawful and patriotic manner.”
—Rutherford Birchard Hayes (1822–1893)