Theory of Quantum Space-Time

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Brody, D C and Hughston, L P. 2005. Theory of Quantum Space-Time. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461(2061), 2679 - 2699. ISSN 1364-5021 [Article]

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Official URL: https://doi.org/10.1098/rspa.2005.1457

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A generalized equivalence principle is put forward according to which space-time symmetries and, internal quantum, symmetries are indistinguishable before symmetry breaking. Based on this principle, a higher-dimensional extension of Minkowski space is proposed and its properties examined. In this scheme the structure of space-time is intrinsically quantum mechanical. It is shown that the causal geometry of such a quantum space-time (QST) possesses a rich hierarchical structure. The natural extension of the Poincare group to QST is investigated. In particular, we prove that the symmetry group of this space is generated in general by a system of irreducible Killing tensors. After the symmetries are broken, the points of the QST can be interpreted as space-time valued operators. The generic point of a QST in the broken symmetry phase then becomes a Minkowski space-time valued operator. Classical space-time emerges as a map from QST to Minkowski space. It is shown that the general such map satisfying appropriate causality-preserving conditions ensuring linearity and Poincare invariance is necessarily a density matrix

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Article

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https://doi.org/10.1098/rspa.2005.1457