Lectures by

Professor Erik van den Ban

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


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.


In the lectures I will start by discussing the theory of induced representations. Mackey's imprimitivity theorem relates spectral measures on homogeneous manifolds for Lie groups to induced representations in Hilbert bundles over such manifolds.
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.