I report the results of three investigations in the fermion Dyson-Schwinger Equations (DSE's) of four-dimensional quantum electrodynamics (QED$\sb4$) and quantum chromodynamics (QCD), using different Ansatze for the boson propagator and the fermion-boson vertex. / The first study compared the effects of four vertex forms (bare $\gamma\sp{\nu}$, renormalized $\gamma\sp{\nu}$, minimal Ball-Chiu (1) and Curtis-Pennington (2)) in the quark propagator DSE, with an infrared-singular gluon propagator, with several forms for the nonperturbative IR behavior of the effective gluon coupling. It was found that, generally, the more naive the vertex Ansatz was, the smaller was the degree of dynamical chiral symmetry breaking (DCSB). Although no vertex appeared to lead to a completely satisfactory relationship between the scale parameter $\Lambda\sb{\sc QCD}$, pion decay constant $f\sb{\pi}$, and quark condensate, all quantities could be found within two standard deviations of their accepted values. / The second study considers an IR-vanishing gluon propagator of the form / In the course of this study, techniques were developed to analyze the chiral phase transition, and to test a Euclidean propagator for confinement. These are applicable to propagators developed under any models, and are arguably of greater importance than the results for the particular models studied. / Finally I give results from an ongoing study of subtractive renormalization in massive strong-coupling quenched QED$\sb4$. The procedure is straightforward to implement and numerically stable. This is the first study in which this technique is used; it will be useful in future DSE studies, whenever renormalization is required in numerical work. / Source: Dissertation Abstracts International, Volume: 55-09, Section: B, page: 3950. / Co-Major Professors: Anthony G. Williams; Donald Robson. / Thesis (Ph.D.)--The Florida State University, 1994.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_77271 |
| Contributors | Hawes, Frederick Thomas., Florida State University |
| Source Sets | Florida State University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | 161 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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