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We investigate $L^1\to L^\infty$ dispersive estimates for the threedimensional Dirac equation with a potential. We also classify the structure ofobstructions at the thresholds of the essential spectrum as being composed of atwo dimensional space of resonances and finitely many eigenfunctions. We showthat, as in the case of the Schr\"odinger evolution, the presence of athreshold obstruction generically leads to a loss of the natural $t^{-\frac32}$decay rate. In this case we show that the solution operator is composed of afinite rank operator that decays at the rate $t^{-\frac12}$ plus a term thatdecays at the rate $t^{-\frac32}$.

Dispersive estimates for Dirac Operators in dimension three with obstructions at threshold energies