László
Lempert, Purdue U., USA Quantizing a Riemannian manifold
Abstract Typically, the first step in the quantization of a physical system is finding a Hilbert space whose vectors represent the quantum states of the system. Assuming we understand the classical configuration space, a Riemannian manifold M, geometric quantization provides a way to construct this Hilbert space. The Kähler version of geometric quantization constructs the quantum Hilbert space as the space of square integrable holomorphic sections of a certain line bundle over the tangent bundle TM, which is often the same thing as holomorphic L^{2} functions on TM. For this to be meaningful, one needs to choose a complex structure on TM and a weight function (because L^{2} refers to a weighted L^{2} space). The talk will discuss my joint results with Szöke
on how one can make these choices and whether the quantum Hilbert spaces
corresponding to different choices are canonically isomorphic.
