Physics – Quantum Physics
Scientific paper
2000-12-19
Comm. Math. Phys. Vol. 226 (2002), pp. 233-268
Physics
Quantum Physics
Final version. To appear in Communications in Mathematical Physics
Scientific paper
10.1007/s002200200607
Let K be a connected Lie group of compact type and let T*(K) be its cotangent bundle. This paper considers geometric quantization of T*(K), first using the vertical polarization and then using a natural Kahler polarization obtained by identifying T*(K) with the complexified group K_C. The first main result is that the Hilbert space obtained by using the Kahler polarization is naturally identifiable with the generalized Segal-Bargmann space introduced by the author from a different point of view, namely that of heat kernels. The second main result is that the pairing map of geometric quantization coincides with the generalized Segal-Bargmann transform introduced by the author. This means that in this case the pairing map is a constant multiple of a unitary map. For both results it is essential that the half-form correction be included when using the Kahler polarization. Together with results of the author with B. Driver, these results may be seen as an instance of "quantization commuting with reduction."
No associations
LandOfFree
Geometric quantization and the generalized Segal-Bargmann transform for Lie groups of compact type does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Geometric quantization and the generalized Segal-Bargmann transform for Lie groups of compact type, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric quantization and the generalized Segal-Bargmann transform for Lie groups of compact type will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-375045