  In this manuscript we study luminescence of hexagonal boron nitride (hBN) by
means of non-equilibrium Green's functions plus time-dependent perturbation
theory. We derive a formula for light emission in solids in the limit of a weak
excitation that includes perturbatively the contribution of electron-phonon
coupling at the first order. This formula is applied to study luminescence in
bulk hBN. This material has attracted interest due to its strong luminescence
in the ultraviolet [Watanabe et al., Nature Mat. 3, 404(2004)]. The origin of
this luminescence has been widely discussed, but only recently has a clear
signature of phonon mediated light emission emerged in the experiments
[Cassabois et al., Nature Phot. 10, 262(2016)]. By means of our new theoretical
approach we provide a clear and full explanation of light emission in hBN.
