Dirac spinors for doubly special relativity and -Minkowski noncommutative spacetime

Abstract

We construct a Dirac equation that is consistent with one of the\nrecently-proposed schemes for a "doubly-special relativity", a relativity with\nboth an observer-independent velocity scale (still naturally identified with\nthe speed-of-light constant) and an observer-independent length/momentum scale\n(possibly given by the Planck length/momentum). We find that the introduction\nof the second observer-independent scale only induces a mild deformation of the\nstructure of Dirac spinors. We also show that our modified Dirac equation\nnaturally arises in constructing a Dirac equation in the kappa-Minkowski\nnoncommutative spacetime. Previous, more heuristic, studies had already argued\nfor a possible role of doubly-special relativity in kappa-Minkowski, but\nremained vague on the nature of the consistency requirements that should be\nimplemented in order to assure the observer-independence of the two scales. We\nfind that a key role is played by the choice of a differential calculus in\nkappa-Minkowski. A much-studied choice of the differential calculus does lead\nto our doubly-special relativity Dirac equation, but a different scenario is\nencountered for another popular choice of differential calculus.\n