SO*(2N) coherent states for loop quantum gravity
Mathematical Physics
2017-09-13 v1 General Relativity and Quantum Cosmology
High Energy Physics - Theory
math.MP
Abstract
A SU(2) intertwiner with N legs can be interpreted as the quantum state of a convex polyhedron with N faces (when working in 3d). We show that the intertwiner Hilbert space carries a representation of the non-compact group SO*(2N). This group can be viewed as the subgroup of the symplectic group Sp(4N,R) which preserves the SU(2) invariance. We construct the associated Perelomov coherent states and discuss the notion of semi-classical limit, which is more subtle that we could expect. Our work completes the work by Freidel and Livine which focused on the U(N) subgroup of SO*(2N).
Cite
@article{arxiv.1701.07519,
title = {SO*(2N) coherent states for loop quantum gravity},
author = {Florian Girelli and Giuseppe Sellaroli},
journal= {arXiv preprint arXiv:1701.07519},
year = {2017}
}
Comments
31 pages, 4 figures