## Citation

Wang, Robert Tung-Hsing
(1976)
*A Study of Some Two-Dimensional Field Theory Models.*
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/XRVY-4Z35.
https://resolver.caltech.edu/CaltechTHESIS:12052017-090641371

## Abstract

Recently it has been pointed out ^{(6)} that quantum
electrodynamics with a massless fermion in one-space, one-time
dimension exhibits behavior which can be interpreted as being
analogous to scaling and confinement. To learn more about
the occurrence of such behavior, we study several other
two-dimensional quantum field theories. After reviewing the
Thirring model, we construct operator solutions of scale-invariant
generalizations with internal degrees of freedom.
We find that the physics of these models can be equally
well described in terms of a field theory of fermions or
of bosons. Because the physical excitations are massless in
these models, the physical states can also be described,
in general, as many-fermion or many-boson states.

We also generalize Lowenstein and Swieca's operator solution of quantum electrodynamics in two-dimensions to a model with more than one massless, charged fermion. Although the resulting physical states are all electrically neutral, we find that the fermions may not be completely confined in the sense that some of their quantum numbers may be represented by particles in the spectrum. Once again, we discover that the physics can be represented by a fermion field theory or by a boson theory.

The fact that the same physics can be represented by interacting fermions or interacting bosons can be understood by considering the polarization fields associated with the fermion charge and axial charge. This general physical picture allows us to extend the fermion-boson duality to theories with non-trivial scattering. Although these models cannot be solved, we can use formal operator structures to test, in a semi-classical approximation, for the possible existence of charged fermion states in the spectrum. Because the fermion states are equivalent to coherent states of bosons, their physics is approximated by solutions to the appropriate classical boson theory. Therefore, in two dimensions, confinement may be a phenomenon associated with the classical behavior of a theory.

Item Type: | Thesis (Dissertation (Ph.D.)) | ||||||||
---|---|---|---|---|---|---|---|---|---|

Subject Keywords: | Physics | ||||||||

Degree Grantor: | California Institute of Technology | ||||||||

Division: | Physics, Mathematics and Astronomy | ||||||||

Major Option: | Physics | ||||||||

Thesis Availability: | Public (worldwide access) | ||||||||

Research Advisor(s): | - Mandula, Jeffrey (advisor)
- Feynman, Richard Phillips (co-advisor)
| ||||||||

Thesis Committee: | - Unknown, Unknown
| ||||||||

Defense Date: | 1 January 1975 | ||||||||

Funders: |
| ||||||||

Record Number: | CaltechTHESIS:12052017-090641371 | ||||||||

Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:12052017-090641371 | ||||||||

DOI: | 10.7907/XRVY-4Z35 | ||||||||

Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||

ID Code: | 10583 | ||||||||

Collection: | CaltechTHESIS | ||||||||

Deposited By: | Benjamin Perez | ||||||||

Deposited On: | 05 Dec 2017 17:30 | ||||||||

Last Modified: | 21 Dec 2019 02:18 |

## Thesis Files

PDF
- Final Version
See Usage Policy. 39MB |

Repository Staff Only: item control page