Polarisation of high energy gamma-rays after scattering
  The polarisation of sunlight after scattering off the atmosphere was first
described by Chandrasekhar using a geometrical description of Rayleigh
interactions. Kosowsky later extended Chandrasekhar's formalism by using
Quantum Field Theory (QFT) to describe the polarisation of the Cosmological
Microwave Background radiation. Here we focus on a case that is rarely
discussed in the literature, namely the polarisation of high energy radiation
after scattering off particles. After demonstrating why the geometrical and low
energy QFT approaches fail in this case, we establish the transport formalism
that allows to describe the change of polarisation of high energy photons when
they propagate through space or the atmosphere. We primarily focus on Compton
interactions but our approach is general enough to describe e.g. the scattering
of high energy photons off new particles or through new interactions. Finally
we determine the conditions for a circularly polarised $\gamma$--ray signal to
keep the same level of circular polarisation as it propagates through its
environment.
