On Minkowski Functionals of CMB polarization
  CMB polarization data is usually analyzed using $E$ and $B$ modes because
they are scalars quantities under rotations along the lines of sight and have
distinct physical origins. We explore the possibility of using the Stokes
parameters $Q$ and $U$ for complementary analysis and consistency checks in the
context of searches for non-Gaussianity. We show that the Minkowski Functionals
(MFs) of $Q,U$ are invariant under local rotations along the lines of sight
even though $Q,U$ are spin-2 variables, for full sky analysis. The invariance
does not hold for incomplete sky. For local type primordial non-Gaussianity,
when we compare the non-Gaussian deviations of MFs for $Q,U$ to what is
obtained for $E$ mode or temperature fluctuations, we find that the amplitude
is about an order of magnitude lower and the shapes of the deviations are
different. This finding can be useful in distinguishing local type
non-Gaussianity from other origins of non-Gaussianity in the observed data.
Lastly, we analyze the sensitivity of the amplitudes of the MFs for $Q$, $U$
and the number density of singularities of the total polarization intensity to
the tensor-to-scalar ratio, $r$, and find that all of them decrease as $r$
increases.
