Aspects Of Quantum Field Theory On A Noncommutative Spacetime

We calculate the photon self energy innoncommutative Schwinger model at first order of the noncommutative parameter and show that it reveals an emergence of a higher derivative operator. We add the higher derivative operator inquestion to the Lagrangian and discuss the problem of unitarity. One recently developed approach for solving the UV/IR mixing is translation invariant models. We address the issue of-Ward identity in this new approach and show by some explicit calculations that there are some poles. Thus, the conventional Ward identity need to be modified in order to take care of those poles. Finally, a new idea towards gravity in noncommutative spacetime was applied to scalar field and gauge field. We extend it to fermion, and show that it does not work. This thesis contains among the results of our investigation an overview of the present situation in the field, a review of star product and its properties, a review of how to construct field theories on noncommutative spacetime, and a brief review of Seiberg-Witten map.