Concentration of measure on the Fubini-Study metric of high-dimensional pure states produces an equidistant dust whose spectral dimension at the single relaxation scale is two, a measurement property shown via Lean-checked Beta-law overlaps rather than evidence for physical 2D spacetime.
Matrix algebras converge to the sphere for quantum Gromov--Hausdorff distance
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abstract
On looking at the literature associated with string theory one finds statements that a sequence of matrix algebras converges to the 2-sphere (or to other spaces). There is often careful bookkeeping with lengths, which suggests that one is dealing with ``quantum metric spaces''. We show how to make these ideas precise by means of Berezin quantization using coherent states. We work in the general setting of integral coadjoint orbits for compact Lie groups.
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gr-qc 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Quantum Dust from the Curse of Dimensionality
Concentration of measure on the Fubini-Study metric of high-dimensional pure states produces an equidistant dust whose spectral dimension at the single relaxation scale is two, a measurement property shown via Lean-checked Beta-law overlaps rather than evidence for physical 2D spacetime.