Dirac spinors for doubly special relativity and κ-Minkowski noncommutative spacetime
Abstract
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 κ-Minkowski noncommutative spacetime. Previous, more heuristic studies had already argued for a possible role of doubly special relativity in κ-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 κ-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.
- Publication:
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Classical and Quantum Gravity
- Pub Date:
- April 2004
- DOI:
- 10.1088/0264-9381/21/8/018
- arXiv:
- arXiv:gr-qc/0207003
- Bibcode:
- 2004CQGra..21.2179A
- Keywords:
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- General Relativity and Quantum Cosmology
- E-Print:
- 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 accordingly