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

Share

COinS