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Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity
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We study the spectrum of the length and area operators in Lorentzian loop quantum gravity, in 2+1 spacetime dimensions. We find that the spectrum of spacelike intervals is continuous, whereas the spectrum of timelike intervals is discrete. This result contradicts the expectation that spacelike intervals are always discrete. On the other hand, it is consistent with the results of the spin foam quantization of the same theory.
Forward citations
Cited by 3 Pith papers
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Indefinite probabilities in quantum spacetime: A deepening of unpredictability
SU_q(2) quantum group applied to spin-1/2 rotations yields non-commuting probability operators, an uncertainty principle for probabilities, and non-commutative rotation matrices between observers.
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Indefinite probabilities in quantum spacetime: A deepening of unpredictability
SU_q(2) rotational symmetry turns spin probabilities into non-commuting operators, yielding an uncertainty principle that prevents sharp measurement of relative observer orientations.
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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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