Representation theory of the Heisenberg group in quantum and classical mechanics
by
Alastair Brodlie
University of Leeds

The infinite dimensional unitary irreducible representations of the Heisenberg group have been at the heart of quantum mechanics since its origin. The one dimensional unitary irreducible representations are usually ignored, and only included in the Stone Von-Neumann theorem for mathematical completeness. We show that the one dimensional representations of the Heisenberg group can play the role in classical mechanics which the infinite dimensional representations play in quantum mechanics. This allows us to exhibit interesting relations between quantum and classical mechanics. The theory is illuminated through the examples of the forced harmonic oscillator and the Kepler problem. Canonical transformations and coherent states are also shown to be of use in the construction

Date received: March 2, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # camv-38.