---

In the framework of studying noncommutative gauge field theory a model with an additional oscillator-like term in the action is discussed, which already like Grosse and Wulkenhaar showed is renormalizable to all orders in the case of a scalar phi^4 model. To be able to write down the propagator of such models one needs roughly speaking the inverse of the operator p^2+x^2. This is the Mehler kernel, which will be discussed in this diploma thesis. Not only a full derivation and different properties of the latter will be given, but also explicitly some loop calculations in a special model where the Mehler kernel is needed will be executed.

---

I, Erwin Kronberger was born on the July 8, 1983 in Vienna and grew up in the small village Grossinzersdorf. After finishing secondary school in Gänserndorf I have studied physics at the Technical University in Vienna and received my master´s degree 2008.

---