Abstract: The vacuum polarization function of the photon describes how quantum effects affect the energy dependence of the electromagnetic coupling. It is a fundamental quantity and also affects many scattering processes in collider physics and the decay of many particles which are unstable. In this project the standard operator product expansion of the vacuum polarization function originally devised by Shifman, Vainshtein and Zakharov will be calculated to all orders in a massive gluon model. The result will then be generalized to a nonlocal operator product expansion based on the gradient flow method, which could show substantially better convergence. It this is true, the new method may find applications in a large range of other important applications in the future.
