We construct a Dirac equation that is consistent with one of the
recently-proposed schemes for a "doubly-special relativity", a relativity with
both an observer-independent velocity scale (still naturally identified with
the speed-of-light constant) and an observer-independent length/momentum scale
(possibly given by the Planck length/momentum). We find that the introduction
of the second observer-independent scale only induces a mild deformation of the
structure of Dirac spinors. We also show that our modified Dirac equation
naturally arises in constructing a Dirac equation in the kappa-Minkowski
noncommutative spacetime. Previous, more heuristic, studies had already argued
for a possible role of doubly-special relativity in kappa-Minkowski, but
remained vague on the nature of the consistency requirements that should be
implemented in order to assure the observer-independence of the two scales. We
find that a key role is played by the choice of a differential calculus in
kappa-Minkowski. A much-studied choice of the differential calculus does lead
to our doubly-special relativity Dirac equation, but a different scenario is
encountered for another popular choice of differential calculus.Comment: 26 pages, LaTex. v2: Alessandra Agostini (contributing some results
from her PhD thesis) is added to the list of authors. The results presented
in v1 remain unchanged and are contained in Section 2. Sections 3,4,5 add
results not present in v1, concerning the realization of the DSR-deformed
Dirac equation in kappa-Minkowski noncommutative spacetime. Title changed
accordingl
