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A useful concept in the development of physical models on the $\kappa$-Minkowski noncommutative spacetime is that of a curved momentum space.
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A. Agostini, G. Amelino-Camelia, and M. Arzano, “Dirac spinors for doubly special relativity and kappa Minkowski noncummutative space-time,” Class. Quant. Grav
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2016
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M. Arzano and M. Laudonio, “Accelerated horizons and Planck-scale kinematics,” Phys. Rev
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F. Mercati and M. Sergola, “Light Cone in a Quantum Spacetime,” Phys. Lett
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D. Jurman, “Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis,” Fortsch. Phys
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M. Daszkiewicz, “Canonical and Lie-algebraic twist deformations of Carroll, para-Galilei and Static Hopf algebras,” Mod. Phys. Lett. A
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