  The free space Maxwell dielectric problem can be reduced to a system of
surface integral equations (SIE). A numerical formulation for the Maxwell
dielectric problem using an SIE system presents two key advantages: first, the
radiation condition at infinity is exactly satisfied, and second, there is no
need to artificially define a truncated domain. Consequently, these SIE systems
have generated much interest in physics, electrical engineering, and
mathematics, and many SIE formulations have been proposed over time.
  In this article we introduce a new SIE formulation which is in the desirable
operator form identity plus compact, is well-posed, and remains
well-conditioned as the frequency tends to zero. The unknowns in the
formulation are three dimensional vector fields on the boundary of the
dielectric body. The SIE studied in this paper is derived from a formulation
developed in earlier work by some of the authors~\cite{ganesh2014all}. Our
initial formulation utilized linear constraints to obtain a uniquely solvable
system for all frequencies. The new SIE introduced and analyzed in this article
combines the integral equations from \cite{ganesh2014all} with new constraints.
We show that the new system is in the operator form identity plus compact in a
particular functional space, and we prove well-posedness at all frequencies and
low-frequency stability of the new SIE.
