Replacing SU(2) with SU_q(2) turns measurement probabilities into operators and makes reference-frame alignment between two observers fundamentally imprecise even in the limit of infinitely many exchanged spins.
De Sitter space as an arena for Doubly Special Relativity
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We show that Doubly Special Relativity (DSR) can be viewed as a theory with energy-momentum space being the four dimensional de Sitter space. Different formulations (bases) of the DSR theory considered so far can be therefore understood as different coordinate systems on this space. The emerging geometrical picture makes it possible to understand the universality of the non-commutative structure of space-time of Doubly Special Relativity. Moreover, it suggests how to construct the most natural DSR bases and makes it possible to address the long standing problem of total momentum of many particle systems from a different perspective.
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Doubly Quantum Mechanics
Replacing SU(2) with SU_q(2) turns measurement probabilities into operators and makes reference-frame alignment between two observers fundamentally imprecise even in the limit of infinitely many exchanged spins.