  The generation of the circular polarization of Gamma Ray Burst (GRB) photons
is discussed in this paper via their interactions with astroparticles in the
presence or absence of background fields such as magnetic fields and
non-commutative space time geometry. Solving quantum Boltzmann equation for
GRB-photons as a photon ensemble, we discuss the generation of circular
polarization (as Faraday conversion phase shift $\Delta \phi_{FC}$) of GRBs in
the following cases: (i) intermediate interactions, i.e. the Compton scattering
of GRBs in the galaxy cluster magnetic field and in the presence of
non-commutative space time geometry, as well as the scattering of GRBs in
cosmic neutrino background (CNB), and in cosmic microwave background (CMB);
(ii) interactions with particles and fields in shock wave, i.e. the Compton
scattering of GRBs with accelerated charged particles in the presence of
magnetic fields. We found that (i) after shock wave crossing, the most
contribution of $\Delta \phi_{FC}$ for energetic GRBs (in order GeV and larger)
comes from GRB-CMB interactions, however for low energy GRBs the contributions
of the Compton scattering of GRBs in the galaxy cluster magnetic field
dominate; (ii) in shock wave crossing, the magnetic filed has significant
effects on converting GRB's linear polarization to circular one, this effect
can be used to better understanding magnetic profile in shock wave. The main
aim of this work is a emphasis that the studying and measuring the circular
polarization of GRBs are helpful for better understanding of physics and
mechanism of the generation of GRBs and their interactions before reaching us.
