Dispersive estimates for massive Dirac operators in dimension two

We study the massive two dimensional Dirac operator with an electric potential. In particular, we show that the t⁻¹ decay rate holds in the L¹→L^∞ setting if the threshold energies are regular. We also show these bounds hold in the presence of s-wave resonances at the threshold. We further show that, if the threshold energies are regular then a faster decay rate of t⁻¹(log⁡t)⁻² is attained for large t, at the cost of logarithmic spatial weights. The free Dirac equation does not satisfy this bound due to the s-wave resonances at the threshold energies.