Abstract
Quantum geometry determines properties of quantized space–time structures, which can be interpreted as providing an atomic understanding of space–time. A view results which is fascinating not only in its physical implications but also in its rich combination of aspects of geometry and quantum theory. Many relevant features can already be seen by analogy with quantized particles, particle then borne out by rigorous constructions of quantum space–time.
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Assuming a sequence of states in \(|\psi_n\rangle\in{\fancyscript{H}}/({{\mathbb{C}}}|0\rangle)\) such that \(\lim_{n\to\infty}|\psi_n\rangle=|0\rangle,\) we obtain the contradiction \(0=\lim_{n\to\infty}\langle 0|\psi_n\rangle=\langle0|\lim_{n\to\infty} \psi_n\rangle=1.\)
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Bojowald, M. (2011). Kinematics: Spatial Atoms. In: Quantum Cosmology. Lecture Notes in Physics, vol 835. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8276-6_3
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