Discrete Gravity in One Dimension

Abstract

A model for quantum gravity in one (time) dimension is discussed, based on Regge's discrete formulation of gravity. The nature of exact continuous lattice diffeomorphisms and the implications for a regularized gravitational measure are examined. After introducing a massless scalar field coupled to the edge lengths, the scalar functional integral is performed exactly on a finite lattice, and the ensuing change in the measure is determined. It is found that the renormalization of the cosmological constant due to the scalar field fluctuations vanishes identically in one dimension. A simple decimation renormalization group transformation is performed on the partition function and the results are compared with the exact solution. Finally the properties of the spectrum of the scalar Laplacian are compared with results obtained for a Poissonian distribution of edge lengths.

23 pages, postscript, 3 figures

References in corpus (1)

• Simplicial Gravity Coupled to Scalar Matter

Cited by in corpus (11)

• Recent Progress in Regge Calculus
• Gauge Invariance in Simplicial Gravity
• Non-Perturbative Gravity and the Spin of the Lattice Graviton
• Faddeev-Popov determinant in 2-dimensional Regge gravity.
• Inconsistencies from a Running Cosmological Constant
• Wheeler-DeWitt Equation in 3 + 1 Dimensions
• Exact Bianchi Identity in Regge Gravity
• Feynman Rules for Simplicial Gravity
• Renormalization of lattice-regularized quantum gravity models I. General considerations
• The principle of stationary action in the calculus of variations
• Path integral in the simplest Regge calculus model