Two Loop Effective Potential of Supersymmetric Quantum Electrodynamics.

The formalism of effective potential method is first studied for usual field theory and extended to supersymmetric field theory. The specific case of supersymmetric quantum electrodynamics is then introduced. The superfields are shifted as required by Weinberg's method for the evaluation of effective potentials and superpropagators are derived with the method developed by Helayel-Neto for cases where supersymmetry is explicitly broken. Then, the one and two loop corrections to the effective potential may be calculated. These corrections are seen to be complex everywhere but at the minimum of the potential. Tile theory is then renormalized in a modified minimal substraction scheme and a finite expression is finally obtained for the effective potential. Thereon, the renormalized coupling constant and the beta-function are calculated.