Degree Type
Honors Capstone Project
Date of Submission
Spring 5-1-2018
Capstone Advisor
Simon Catterall
Honors Reader
John Laiho
Capstone Major
Physics
Capstone College
Arts and Science
Audio/Visual Component
no
Capstone Prize Winner
no
Won Capstone Funding
no
Honors Categories
Sciences and Engineering
Subject Categories
Elementary Particles and Fields and String Theory | Physical Sciences and Mathematics | Physics
Abstract
We study the nonperturbative formulation of three-dimensional Euclidean quantum gravity defined via dynamical triangulations (DT). A lattice representation of the Einstein-Hilbert action is modified to include a nontrivial local measure term with free parameter �. We’ve used Monte Carlo and finite-size scaling techniques to locate and analyze the corresponding phase diagram, finding evidence of two metastable states separated by a line of first-order geometric transitions. After fine-tuning the bare couplings to values near this boundary, the running latent heat, as measured by the distance between peaks in a histogram of our order parameter, is shown to grow smaller as � decreases. Preliminary calculations of the spectral dimension indicate geometries in this region correspond to highly fractal branched polymers of baby universes. The latter suggests that while an interesting three-dimensional continuum limit may still be recovered at sufficiently large �, the unphysical nature of this phase makes it a poor candidate for realizing a quantum field theory of general relativity
Recommended Citation
Chevalier, Cameron, "Dynamically Triangulated Quantum Gravity in Three Dimensions" (2018). Renée Crown University Honors Thesis Projects - All. 1181.
https://surface.syr.edu/honors_capstone/1181
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