Born-corrections to weak lensing of the cosmic microwave background
  temperature and polarisation anisotropies
  Many weak lensing calculations make use of the Born approximation where the
light ray is approximated by a straight path. We examine the effect of
Born-corrections for lensing of the cosmic microwave background in an
analytical approach by taking perturbative corrections to the geodesic into
account. The resulting extra power in the lensing potential spectrum is
comparable to the power generated by nonlinear structure formation and affects
especially the polarisation spectra, leading to relative changes of the order
of one per cent for the $E$-mode spectrum and up to 10 per cent on all scales
to the $B$-mode spectrum. In contrast, there is only little change of spectra
involving the CMB temperature. Additionally, the corrections excite one more
degree of freedom resulting in a deflection component which can not be
described as a gradient of the lensing potential as it is related to image
rotation in lens-lens coupling. We estimate the magnitude of this effect on the
CMB-spectra and find it to be negligible.
