I'm wondering if there are cases of discretization models (in lattices or graphs) that converge toward the nonlinear Dirac equations? While there is a paper on the 2d and 3d cases http://arxiv.org/abs/1307.3524 here, there is no work done on quantum random walk models for the nonlinear cases. In case anyone needs some info, the Dirac equation is a 1st order solution to the more known 2nd order KleinGordon equation: http://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation. Ignoring the light and quantum constants by setting them 1, the Dirac equation also has a more generalized solution, which is replacing the mass m with m*(cosp+sigma(z)*i*sinp) instead, which I have found to have a discrete model.
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