Geometric quantization and semi-classical limits of pairings of TQFT vectors
Geometric Topology
2014-12-16 v1 Mathematical Physics
math.MP
Symplectic Geometry
Abstract
Using geometric quantization, we represent curve operators in the TQFT of Witten-Reshetikhin-Turaev with jauge group SU_2 as Toeplitz operators with symbols corresponding to trace functions. As an application, we show that eigenvectors of these operators are concentrated near the level sets of these trace functions, and obtain asymptotic estimates of pairings of such eigenvectors. This yields an asymptotic for some matrix coefficients of the image of mapping classes by quantum representations.
Keywords
Cite
@article{arxiv.1412.4333,
title = {Geometric quantization and semi-classical limits of pairings of TQFT vectors},
author = {Renaud Detcherry},
journal= {arXiv preprint arXiv:1412.4333},
year = {2014}
}