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Algebraic approach to quantum gravity II: noncommutative spacetime
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We provide a self-contained introduction to the quantum group approach to noncommutative geometry as the next-to-classical effective geometry that might be expected from any successful quantum gravity theory. We focus particularly on a thorough account of the bicrossproduct model noncommutative spacetimes of the form [t,x_i]=i \lambda x_i and the correct formulation of predictions for it including a variable speed of light. We also study global issues in the Poincar\'e group in the model with the 2D case as illustration. We show that any off-shell momentum can be boosted to infinite negative energy by a finite Lorentz transformaton.
Forward citations
Cited by 2 Pith papers
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Indefinite probabilities in quantum spacetime: A deepening of unpredictability
Using the SU_q(2) quantum group for spin rotations yields non-commuting probability operators, implying indefinite probabilities and preventing sharp determination of relative observer orientations.
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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.
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