  This letter assigns the Faraday rotation in photoexcited semiconductors to
``Pauli interactions'', \emph{i}. \emph{e}., carrier exchanges, between the
real excitons present in the sample and the virtual excitons coupled to the
$\sigma_{\pm}$ parts of a linearly polarized light. While \emph{direct Coulomb}
interactions scatter bright excitons into bright excitons, whatever their spins
are, \emph{Pauli} interactions do it for bright excitons \emph{with same spin
only}. This makes these Pauli interactions entirely responsible for the
refractive index difference, which comes from processes in which the virtual
exciton which is created and the one which recombines are formed with different
carriers. To write this difference in terms of photon detuning and exciton
density, we use our new many-body theory for interacting excitons. Its multiarm
``Shiva'' diagrams for $N$-body exchanges make transparent the physics involved
in the various terms. This work also shows the interesting link which exists
between Faraday rotation and the exciton optical Stark effect.
