Dirac spinors for Doubly Special Relativity and $\kappa$-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 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.

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

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• On the 5D differential calculus and translation transformations in 4D kappa-Minkowski noncommutative spacetime
• Effects of quantum deformation on the integer quantum Hall effect
• Chiral bosonization for non-commutative fields
• Effects of quantum deformation on the Jaynes-Cummings and anti-Jaynes-Cummings models
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• Photonic realization of the kappa-deformed Dirac equation
• Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Quantisation of $\kappa$-deformed Dirac equation
• The Weyl-Mellin quantization map for $\kappa$-Minkowski Noncommutative Spacetime
• Parity at the Planck scale
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