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.