The Mehler Kernel

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.

Autorentext

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.