  We show that, by going beyond the low-energy approximation for which the
dispersion relations of graphene are linear, the corresponding emergent field
theory is a specific generalization a Dirac field theory. The generalized Dirac
Hamiltonians one obtains are those compatible with specific generalizations of
the uncertainty principle. We also briefly comment on the compatibility of the
latter with noncommuting positions, $[x_i,x_j] \neq 0$, and on their possible
physical realization.
