We investigate L1 →L∞ dispersive estimates for the three dimensional Dirac equation with a potential. We also classify the structure of obstructions at the thresholds of the essential spectrum as being composed of a two dimensional space of resonances and finitely many eigenfunctions. We show that, as in the case of the Schrodinger evolution, the presence of a threshold obstruction generically leads to a loss of the natural t-3/2 decay rate. In this case we show that the solution operator is composed of a finite rank operator that decays at the rate t-1/2 plus a term that decays at the rate t-3/2.
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