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arXiv · 1810.10831

Quantum gravity on a square graph

Shahn Majid
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Abstract

We consider functional-integral quantisation of the moduli of all quantum metrics defined as square-lengths $a$ on the edges of a Lorentzian square graph. We determine correlation functions and find a fixed relative uncertainty $\Delta a/ = 1/\sqrt{8}$ for the edge square-lengths relative to their expected value $ $. The expected value of the geometry is a rectangle where parallel edges have the same square-length. We compare with the simpler theory of a quantum scalar field on such a rectangular background. We also look at quantum metric fluctuations relative to a rectangular background, a theory which is finite and interpolates between the scalar theory and the fully fluctuating theory.

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Shahn Majid. 2018-10-25. Quantum gravity on a square graph. https://doi.org/10.1088/1361-6382%2Fab4975

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