Operator product expansion

Encyclopedia : O : OP : OPE : Operator product expansion

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/

[A(x)B(y)=\sum_c_i(x-y)C^i(y)]

where the sum is over finitely or countably many terms, Cⁱ are operator-valued fields, c_i are analytic functions over O/ and the sum is convergent in the operator topology within O/.

OPEs are most often used in conformal field theory.

The notation [F(x,y)\sim G(x,y)] 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.

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