Document Type
Dissertation
Date of Degree
Spring 2017
Degree Name
PhD (Doctor of Philosophy)
Degree In
Applied Mathematical and Computational Sciences
First Advisor
Wayne Polyzou
Abstract
This thesis investigates the use of Daubechies wavelets to separate scales in local quantum field theory. Field theories have an infinite number of degrees of freedom on all distance scales. Quantum field theories are believed to describe the physics of subatomic particles. These theories have no known mathematically convergent approximation methods. Daubechies wavelet bases can be used separate degrees of freedom on different distance scales. Volume and resolution truncations lead to mathematically well-defined truncated theories that can be treated using established methods. This work demonstrates that flow equation methods can be used to block diagonalize truncated field theoretic Hamiltonians by scale. This eliminates the fine scale degrees of freedom. This may lead to approximation methods and provide an understanding of how to formulate well-defined fine resolution limits.
Keywords
flow equation, quantum field theory, wavelets
Pages
ix, 69 pages
Bibliography
Includes bibliographical references (pages 65-69).
Copyright
Copyright © 2017 Tracie L. Michlin