  The relationship between finite volume multi-hadron energy levels and matrix
elements and two particle scattering phase shifts and decays is well known, but
the inclusion of long range interactions such as QED is non-trivial. Inclusion
of QED is an important systematic error correction to $K\to\pi\pi$ decays. In
this talk, we present a method of including a truncated, finite-range Coulomb
interaction in a finite-volume lattice QCD calculation. We show how the
omission caused by the truncation can be restored by an infinite-volume
analytic calculation so that the final result contains no power-law
finite-volume errors beyond those usually present in Luscher's finite-volume
phase shift determination. This approach allows us to calculate the QED
corrected infinite-volume phase shift for $\pi\pi$ scattering in Coulomb gauge,
a necessary ingredient to $K\to\pi\pi$, while neglecting the transverse
radiation for now.

High Energy Physics - Lattice