Quantum gravity on a square graph

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 $\Delta a/<a>=1/\sqrt{8}$ for the edge square-lengths relative to their expected value $<a>$. 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.

17 pages latex, 2 pdf figures

References in corpus (6)

• Loop quantum cosmology of k=1 FRW models
• Generalised Chern-Simons actions for 3d gravity and kappa-Poincare symmetry
• Quantum Riemannian geometry and particle creation on the integer line
• Spectral estimators for finite non-commutative geometries
• Quasitriangular structure and twisting of the 2+1 bicrossproduct model
• On the emergence of the structure of Physics

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