**Lectures by **

** Department of Mathematics**

**University of Utrecht**

A PhD-course under the National PhD-school in Geometry and Mathematical Physics, GEOMAPS

Erik van den Ban will give a series of lectures with the title:

**Application of representation
theory in quantum mechanics**

**The lectures take
place
at the Department of
Mathematical Sciences, University of Copenhagen**

Schedule:

Wednesday, June 11, 2008, 10.15 - 12.00 in Aud. 9,

Wednesday, June 11, 2008, 13.15 - 14.00 in Aud. 8,

Friday, June 13, 2008, 10.15 - 12.00 in Aud. 8.

**Abstract**

Following Mackey I will then use the imprimitivity theorem to describe the irreducible unitary representations of a semi-direct product of the form G = H x N with H a closed and N an abelian closed normal subgroup of G.

In the final lecture I will discuss the structure of the Lorentz and the Poincar\'e group. I will then show how application of Mackey's theorem leads to Wigner's theorem, which describes the physically relevant representations of the Poincar\'e group.

The lectures will be based on notes that can be downloaded from here.