  A new integral equation formulation is presented for the Maxwell transmission
problem in Lipschitz domains. It builds on the Cauchy integral for the Dirac
equation, is free from false eigenwavenumbers for a wider range of
permittivities than other known formulations, can be used for magnetic
materials, is applicable in both two and three dimensions, and does not suffer
from any low-frequency breakdown. Numerical results for the two-dimensional
version of the formulation, including examples featuring surface plasmon waves,
demonstrate competitiveness relative to state-of-the-art integral formulations
that are constrained to two dimensions. However, our Dirac integral equation
performs equally well in three dimensions, as demonstrated in a companion
paper.
