| dc.description.abstract | The Orbit Method is a method to determine all irreducible unitary representations
of a Lie group. It is entangled with its physical counterpart geometric
quantization, which is an extension of the canonical quantization scheme to
general curved manifolds. The main ingredient of the Orbit Method is the
notion of coadjoint orbits, which will be explained. Coadjoint orbits of a Lie
group have the natural structure of a symplectic manifold, as does the phase
space of a classical mechanical system. Naturally, geometric quantization
will be treated next, since it attempts to provide a geometric interpretation
of quantization within an extension of the mathematical framework of classical
mechanics (symplectic geometry). In particular, the axioms imposed on
a quantization will be discussed. Finally, as an application, coadjoint orbits
and geometric quantization will be brought together by indicating how to
determine the irreducible unitary representations of SU(2) by means of the
Orbit Method. | |
