Branes, Quantization and Fuzzy Spheres
Abstract
We propose generalized quantization axioms for Nambu-Poisson manifolds, which allow for a geometric interpretation of n-Lie algebras and their enveloping algebras. We illustrate these axioms by describing extensions of Berezin-Toeplitz quantization to produce various examples of quantum spaces of relevance to the dynamics of M-branes, such as fuzzy spheres in diverse dimensions. We briefly describe preliminary steps towards making the notion of quantized 2-plectic manifolds rigorous by extending the groupoid approach to quantization of symplectic manifolds.
Keywords
Cite
@article{arxiv.1101.5987,
title = {Branes, Quantization and Fuzzy Spheres},
author = {Christian Saemann and Richard J. Szabo},
journal= {arXiv preprint arXiv:1101.5987},
year = {2011}
}
Comments
18 pages; Based on Review Talk at the Workshop on "Noncommutative Field Theory and Gravity", Corfu Summer Institute on Elementary Particles and Physics, September 8-12, 2010, Corfu, Greece; to be published in Proceedings of Science