An Obstruction to Quantizing Compact Symplectic Manifolds
dg-ga
2008-02-03 v3 Differential Geometry
Quantum Physics
Abstract
We prove that there are no nontrivial finite-dimensional Lie representations of certain Poisson algebras of polynomials on a compact symplectic manifold. This result is used to establish the existence of a universal obstruction to quantizing a compact symplectic manifold, regardless of the dimensionality of the representation.
Keywords
Cite
@article{arxiv.dg-ga/9706001,
title = {An Obstruction to Quantizing Compact Symplectic Manifolds},
author = {Mark J. Gotay and Janusz Grabowski and Hendrik B. Grundling},
journal= {arXiv preprint arXiv:dg-ga/9706001},
year = {2008}
}
Comments
LaTeX2e, 9 pps. Uses amsmath & amsfonts packages. This paper is a revised version of the published article; the proof of Theorem 4 has been redone and simplified