Dissertation
Finite ϕ^4 in the medium-coupling regime
University of Iowa
Doctor of Philosophy (PhD), University of Iowa
Spring 2024
DOI: 10.25820/etd.007426
Abstract
We discuss the inherent challenges at the current frontier of quantum field theory (QFT), exploring both the well-known limitations of perturbative approaches and the less obvious limitations of non-perturbative approaches, both of which are exacerbated in many cases of particular interest such as in quantum chromodynamics. Motivated by the necessity-in-practice of using a field cutoff, we investigate the relatively unexamined theory of field operators of finite matrix rank, working within the simplest case of lattice \phi^{4} theory as an exemplar and toy model, and explain in detail how a finite operator results in a nonzero radius of convergence. The thesis then delves into the precise shape of the region of convergence in significantly more detail, introducing the concept of exceptional points and leveraging them to introduce a novel method of quickly estimating the radius of covergence of the weak-field perturbative series. In particular, we note that the positive real axis seems to be entirely clear of obstructions; the remainder of the thesis then details and implements a method to generate an analytic continuation of the model that includes both the weak- and strong-field limits, with good convergence throughout the otherwise inaccessible medium-coupling regime.
Details
- Title: Subtitle
- Finite ϕ^4 in the medium-coupling regime
- Creators
- Robert Maxton
- Contributors
- Yannick Meurice (Advisor)Vincent Rodgers (Committee Member)Frauke Bleher (Committee Member)Craig Pryor (Committee Member)Wayne Polyzou (Committee Member)
- Resource Type
- Dissertation
- Degree Awarded
- Doctor of Philosophy (PhD), University of Iowa
- Degree in
- Physics
- Date degree season
- Spring 2024
- DOI
- 10.25820/etd.007426
- Publisher
- University of Iowa
- Number of pages
- x,111 pages
- Copyright
- Copyright 2024 Robert Maxton
- Language
- English
- Description illustrations
- illustrations, graphs
- Description bibliographic
- Includes bibliographical references (pages 110-111).
- Public Abstract (ETD)
- In the world of quantum physics, understanding the fundamental forces and particles of the universe is a complex and fascinating challenge. Quantum field theory (QFT) is a powerful tool in this quest, but it faces significant hurdles, especially when trying to describe certain phenomena like the behavior of quarks and gluons (the building blocks of protons and neutrons) in quantum chromodynamics, a key part of our understanding of the subatomic world. Traditionally, physicists have used two main methods in QFT: perturbative and non-perturbative ap proaches. However, both have limitations, particularly when dealing with complex scenarios. To address these challenges, my research explores a relatively new idea in the field: finite-sized field operators, which replace quantum fields–natively infinite objects–with finite-dimensional approximations. Using a simplified model known as lattice ϕ 4 theory, which acts like a ’toy model’ of the quantum world, I delve into how these finite operators can offer a clearer and more practical way to understand quantum fields. One key discovery is that the region of convergence–the bounds within which we can predict the behavior of quantum fields with confidence–is greatly expanded by the restriction to finite approximations. In fact, the region of con vergence is expanded enough to open the possibility of a solution to ϕ 4 that escapes both the limitations of perturbative and standard non-perturbative approaches; my thesis concerns itself primarily with a practical demonstration of this new approach.
- Academic Unit
- Physics and Astronomy
- Record Identifier
- 9984647456202771
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