Numerical quantum gravity by dynamical triangulation

TL;DR

This paper discusses a new numerical approach called dynamical triangulation for quantum gravity, which modifies geometry by adding or removing simplices, addressing issues in traditional methods but introducing new challenges in maintaining complex integrity.

Contribution

It introduces dynamical triangulation as an alternative to Regge calculus, highlighting its advantages and the need for additional constraints to preserve simplicial structures during simulations.

Findings

Dynamical triangulation modifies geometry via simplices.

Simulations show significant violations of simplicial structure.

Additional conditions are needed to maintain complex topology.

Abstract

Recently an alternate technique for numerical quantum gravity, dynamical triangulation, has been developed. In this method, the geometry is varied by adding and subtracting equilateral simplices from the simplicial complex. This method overcomes certain difficulties associated with the traditional approach in Regge calculus of varying geometry by varying edge lengths. However additional complications are introduced: three of the four moves in dynamical triangulation can violate the simplicial nature of the complex. Simulations indicate that the rate of these violations is significant. Thus additional conditions must be placed on the dynamical triangulation moves to ensure that the simplicial complex and its topology are preserved.