The structure of positronium is governed almost completely by QED; strong and weak corrections are small compared to electrodynamic effects. This makes it an ideal laboratory for studying QED and the bound state formalism in quantum field theory. The objective of the research is to study the energy levels and decay rates in positronium. The emphasis will be on the calculation of order alpha2 corrections to these energy levels and decay rates and to complete the evaluation of the n=1 and n=2 positronium energy levels through order m*alpha2. Completion of these calculations will provide an important test of the bound state formalism and QED.
