Operator product development

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In quantum field theory , operator product development (OPE) is a method for representing a product of two operators at different spacetime points as a series of operators at a single spacetime point. The coefficients of these operators are functions of the difference between the two spacetime points and are called Wilson coefficients according to Kenneth Wilson . Mathematically, the operator product development is:

The operators contain the information about the physics on short distances, the coefficients the information about the physics on large length scales.

Example: Fermi interaction

An application example for an operator product development is the (historical) Fermi interaction which represents an operator product development for two charged Dirac currents and a massive photon propagator. Then:

In the Fermi interaction, this series is broken off after the first summand, because the Fermi theory of the weak interaction was established for .


  • Matthew D. Schwartz: Quantum Field Theory and the Standard Model . Cambridge University Press, New York 2014, ISBN 978-1-107-03473-0 .