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We are interested in the cubic Dirac equation in two space dimensions. Weestablish the small data global existence and sharp pointwise decay results forgeneral cubic nonlinearities without additional structure. We also prove thescattering of the Dirac equation for certain classes of nonlinearities. In allthe above results we do not require the initial data to have compact support.

Global solutions of 2-D cubic Dirac equation with non-compactly supported data