Name: Atsushi Naruko
 Institution: Yukawa Institute for Theoretical Physics 
 Title: second order Boltzmann equation with polarization 
 Key Words: CMB, cosmological perturbation, non-Gaussianity
 Abstract: The second order Boltzmann equation with polarization
 is derived without specifying any gauges.
The distribution function of polarized radiation is discribed
 by a tensor-valued distribution function.
After discussing the gauge transformation property of
 various geometrical quantities and the distribution function at second order,
 we explicitly show the gauge invariance of the resulting equation.