Groupoid Quantization of Loop Spaces
arXiv:1203.5921
Abstract
We review the various contexts in which quantized 2-plectic manifolds are expected to appear within closed string theory and M-theory. We then discuss how the quantization of a 2-plectic manifold can be reduced to ordinary quantization of its loop space, which is a symplectic manifold. We demonstrate how the latter can be quantized using groupoids. After reviewing the necessary background, we present the groupoid quantization of the loop space of R^3 in some detail.
19 pages, Proceedings of the Corfu Summer Institute 2011 - School and Workshops on Elementary Particle Physics and Gravity, September 4-18, 2011, Corfu, Greece