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$π-π$ scattering, QED and finite-volume quantization

Using the Coulomb gauge formulation of QED we present a lattice QCD procedure to calculate the $π^+π^+$ scattering phase shift including the effects of the Coulomb potential which appears in this formulation. The approach described here incorporates the effects of relativity and avoids finite-volume corrections that vanish as a power of the volume in which the lattice calculation is performed. This is the first step in developing a complete lattice QCD calculation of the electromagnetic and isospin-breaking light-quark mass contributions to $\varepsilon'$, the parameter describing direct CP violating effects in $K_L\toππ$ decay.