Calculations in supersymmetric quantum theories

Supersymmetric models which are based on ordinary quantum- mechanical systems, of the form originally suggested by Witten, are studied. Ground-state energy is chosen as a suitable measure of the extent of spontaneous supersymmetry breaking Insight into the mechanism by which such breaking can occur is also sought. Several existing methods for estimating ground state energies are reviewed and compared with the true value, and then some new methods are developed. At first, the canonical T'amiltonian formulation of the models is used, but later the path-integral approach is also considered. In the latter it is shown that the use of a larger family of classical solutions of the equations of motion than customary may be used to improve the normal semi classical calculation. Analogous solutions exist in CP(^n-1) model field theories. Classical, properties of these are discussed, and their potential use in semiclassical calculations similar to the quantum-mechanical ones indicated, Finally we return to super symmetric quantum, mechanics in order to generalise the original structure to cases with many degrees of freedom.