Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Physics and Astronomy

First Advisor

James P. Vary


The history and conceptual development of relativistic two-body formalisms leading up to the Bethe-Salpeter equation are reviewed. The various three dimensional reductions of the Bethe-Salpeter equation, in particular the quasipotential equations, and methods for solving them are discussed. Previous studies which attempted to assess the relative merits of the various equations are examined, and a new criterion for judging the equations is proposed. The bound state energy predictions of the traditional quasipotential equations are compared with the predictions of fourth order perturbation theory at small coupling. The equations are ranked according to how well they reproduce perturbation theory at low coupling. Beyond this, it is shown that the traditional quasipotential equations can be considered to be special cases of a new generalized equation written in terms of three parameters. The parameters of the generalized quasipotential equation are adjusted to construct an equation that does better than the traditional equations at reproducing the predictions of perturbation theory. The intermediate coupling behaviour of the equations is examined by performing fits to the heavy meson spectra and predicting the masses of meson states yet undiscovered. The deep binding limits of relativistic equations are compared and contrasted in the context of Higgs interactions between heavy fermions.



Digital Repository @ Iowa State University,

Copyright Owner

Alan James Sommerer



Proquest ID


File Format


File Size

149 pages

Included in

Nuclear Commons