Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives
High Energy Physics - Theory
2008-11-26 v2
Abstract
We generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S^2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space.
Keywords
Cite
@article{arxiv.hep-th/0611209,
title = {Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives},
author = {Brian P. Dolan and Idrish Huet and Sean Murray and Denjoe O'Connor},
journal= {arXiv preprint arXiv:hep-th/0611209},
year = {2008}
}
Comments
34 pages, v2 contains minor corrections to the published version