The transfer matrix in four-dimensional CDT

Abstract

The Causal Dynamical Triangulation model of quantum gravity (CDT) has a transfer matrix, relating spatial geometries at adjacent (discrete lattice) times. The transfer matrix uniquely determines the theory. We show that the measurements of the scale factor of the (CDT) universe are well described by an effective transfer matrix where the matrix elements are labeled only by the scale factor. Using computer simulations we determine the effective transfer matrix elements and show how they relate to an effective minisuperspace action at all scales.

32 pages, 19 figures

References in corpus (3)

• A second-order phase transition in CDT
• General Covariance in Gravity at a Lifshitz Point
• The Semiclassical Limit of Causal Dynamical Triangulations

Cited by in corpus (16)

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• Towards an UV fixed point in CDT gravity
• CDT and Cosmology
• Renormalization of lattice-regularized quantum gravity models II. The case of causal dynamical triangulations
• The microscopic structure of 2D CDT coupled to matter
• Capturing the phase diagram of (2+1)-dimensional CDT using a balls-in-boxes model
• Topology induced first-order phase transitions in lattice quantum gravity
• Cosmology in Lorentzian Regge calculus: causality violations, massless scalar field and discrete dynamics
• The spectral dimension in 2D CDT gravity coupled to scalar fields
• A second look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations
• Making the case for causal dynamical triangulations
• Landau Theory of Causal Dynamical Triangulations