  We determine the light quark masses from lattice QCD simulations
incorporating the electromagnetic interaction of valence quarks. The meson
masses are calculated on lattice QCD configurations generated by the RBC
Collaboration for two flavors of dynamical domain wall fermions, which are
combined with QED configurations generated via quenched non-compact lattice
QED. The electromagnetic part of the pion mass splitting is found to be
$m_{\pi^+}-m_{\pi^0}=4.12(21)$ MeV, where only the statistical error is quoted,
and similarly for the kaon, 1.443(55) MeV. Our results for the light quark
masses are $m_u^{\rm\bar{MS}}$(2 GeV)=$3.02(27)(19)$ MeV, $m_d^{\rm\bar{MS}}$(2
GeV)=$5.49(20)(34)$ MeV, and $m_s^{\rm\bar{MS}}$(2 GeV)=$119.5(56)(74)$ MeV,
where the first error is statistical and the second systematic. By averaging
over $\pm e$ to cancel ${\cal O}(e)$ noise exactly on each combined gauge field
configuration, we are able to work at physical $\alpha=1/137$ and obtain very
small statistical errors. In our calculation, several sources of systematic
error remain, including finite volume, non-zero lattice spacing, chiral
extrapolation, quenched QED, and quenched strange quark, which may be more
significant than the errors quoted above.
