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A density matrix is defined using coherent states for space-times with apparent horizons.
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Dasgupta, A. Semiclassical quantisation of space-times with apparent horizons, Class. Quant. Grav. 23 635-671 (2006)
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Bahr, B; Thiemann, T. Gauge-invariant coherent states for loop quantum gravity. II. Non-Abelian gauge groups. arXiv: 0709:4636 [gr-qc]
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