Monte Carlo studies of field theory and quantum gravity

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)




Simon M. Catterall


Field theory, Quantum gravity

Subject Categories

Elementary Particles and Fields and String Theory | Physical Sciences and Mathematics | Physics


In this dissertation I describe three main research projects in which I have participated as a graduate student. They share the common theme of using Monte Carlo computer simulation to investigate quantum field theories. I begin by giving a brief review of Monte Carlo simulation as a discrete path integral approach to a quantum theory. Two of the projects involve tests of the Monte Carlo renormalization group method, a systematic way of integrating out short distance features of a physical system in order to gain insight about its critical behavior, and hence its continuum limit. After a review of the ideas of the renormalization group, I discuss our thorough investigation of Monte Carlo renormalization of [straight phi] 4 field theory on a two-dimensional square lattice. The second renormalization project overlaps with the other main thrust of my research, studying quantum gravity as the continuum limit of a sum over all possible ways of piecing together discrete simplices, or simplicial quantum gravity. I describe a unique Monte Carlo renormalization group study of scalar fields coupled to two-dimensional quantum gravity, where we were able to extract the anomalous field dimension for a case inaccessible to analytic methods. Finally I discuss a study of four-dimensional quantum gravity coupled to gauge fields and special concerns one must be aware of when measuring connected correlators in fluctuating geometry.


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