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.^[1] As an axiom, it offers a non-perturbative approach to quantum field theory. One example is the vertex operator algebra, which has been used to construct two-dimensional conformal field theories. 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.^[2]

^ Di Francesco, Philippe; Mathieu, Pierre; Sénéchal, David (1997). Conformal field theory. Graduate texts in contemporary physics. New York: Springer. pp. 127–149. ISBN 978-0-387-94785-3.
^ Hollands, Stefan; Wald, Robert M. (2023-12-02). "The Operator Product Expansion in Quantum Field Theory". arXiv:2312.01096 [hep-th].

[:0-1] Di Francesco, Philippe; Mathieu, Pierre; Sénéchal, David (1997). Conformal field theory. Graduate texts in contemporary physics. New York: Springer. pp. 127–149. ISBN 978-0-387-94785-3.

[2] Hollands, Stefan; Wald, Robert M. (2023-12-02). "The Operator Product Expansion in Quantum Field Theory". arXiv:2312.01096 [hep-th].

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