Dirac spinors for Doubly Special Relativity and $κ$-Minkowski noncommutative spacetime

Details Dirac spinors for Doubly Special Relativity and $κ$-Minkowski noncommutative spacetime Dirac spinors for Doubly Special Relativity and $κ$-Minkowski noncommutative spacetime

2002-06-29

arxiv.org/abs/gr-qc/0207003v2

Class.Quant.Grav. 21 (2004) 2179-2202

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

26 pages, LaTex. v2: Alessandra Agostini (contributing some results from her PhD thesis) is added to the list of authors. The

Scientific paper

10.1088/0264-9381/21/8/018

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.

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