Operator product expansion
In quantum field theory, the operator product expansion (OPE) is used as an axiom to define the product of fields as a sum over the same fields. As an axiom, it offers a non-perturbative approach to quantum field theory. One example is the vertex operator algebra, which has been successfully used to construct conformal field theory. Whether this result can be extended to QFT in general, thus resolving many of the difficulties of a perturbative approach, remains an open research question.
In practical calculations, such as those needed for scattering amplitudes in various collider experiments, the operator product expansion is used in QCD sum rules to combine results from both perturbative and non-perturbative (condensate) calculations.
In 2D Euclidean field theory, the operator product expansion is a Laurent series expansion associated to two operators. A Laurent series is a generalization of the Taylor series in that finitely many powers of the inverse of the expansion variable(s) are added to the Taylor series: pole(s) of finite order(s) are added to the series.
Heuristically, in quantum field theory one is interested in the result of physical observables represented by operators. If one wants to know the result of making two physical observations at two points and , one can time order these operators in increasing time.
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