| This dissertation presents perturbative and nonperturbative aspects of noncommutative (NC) field theories, as well as superalgebras in NC field theory and higher dimensional theories. In particular, the perturbative structures of the NC Wess-Zumino model are investigated in detail, as well as the deformed superalgebra relations of the model. NC solitons in scalar field theory are quantized and quantum corrections to the energy are calculated, where UV-IR divergences are found similar to those in the perturbative theory. Kostant equations in higher dimensions are constructed with differential form representations, in which the solutions are also expressed. |
