  The modeling and removal of foregrounds poses a major challenge to searches
for signals from inflation using the cosmic microwave background (CMB). In
particular, the modeling of CMB foregrounds including various spatial averaging
effects introduces multiple complications that will have to be accounted for in
upcoming analyses. In this work, we introduce the generalization of the
intensity moment expansion to the spin-2 field of linear polarization: the
spin-moment expansion. Within this framework, moments become spin-2 objects
that are directly related to the underlying spectral parameters and
polarization angle distribution functions. In obtaining the required
expressions for the polarization modeling, we highlight the similarities and
differences with the intensity moment methods. A spinor rotation in the complex
plane with frequency naturally arises from the first order moment when the
signal contains both spectral parameters and polarization angle variations.
Additional dependencies are introduced at higher order, and we demonstrate how
these can be accounted with several illustrative examples. Our new modeling of
the polarized signals reveals to be a powerful tool to model the frequency
dependence of the polarization angle. As such, it can be immediately applied to
numerous astrophysical situations.
