Non-commutative ADE geometries as holomorphic wave equations
High Energy Physics - Theory
2009-11-11 v2
Abstract
Borrowing ideas from the relation between classical and quantum mechanics, we study a non-commutative elevation of the ADE geometries involved in building Calabi-Yau manifolds. We derive the corresponding geometric hamiltonians and the holomorphic wave equations representing these non-commutative geometries. The spectrum of the holomorphic waves is interpreted as the quantum moduli space. Quantum A_1 geometry is analyzed in some details and is found to be linked to the Whittaker differential equation.
Cite
@article{arxiv.hep-th/0504049,
title = {Non-commutative ADE geometries as holomorphic wave equations},
author = {Adil Belhaj and Jorgen Rasmussen and El Hassan Saidi and Abdellah Sebbar},
journal= {arXiv preprint arXiv:hep-th/0504049},
year = {2009}
}
Comments
17 pages, v2: version to be published