Dirac spinors for Doubly Special Relativity

We construct a Dirac equation that is consistent with one of the recently-proposed schemes for relativistic transformations with two observer-independent scales (a velocity scale, still naturally identified with the speed-of-light constant, and a length/momentum scale, possibly given by the Planck length/momentum). We exploit the fact that in the energy-momentum sector the transformation laws are governed by a nonlinear realization of the Lorentz group. We find that the nonlinearity, which is due to the introduction of the second observer-independent scale, only induces a mild deformation of the structure of Dirac spinors.