Supersymmetric quantum theory and non-commutative geometry
Abstract
Classical differential geometry can be encoded in spectral data, such as Connes' spectral triples, involving supersymmetry algebras. In this paper, we formulate non-commutative geometry in terms of supersymmetric spectral data. This leads to generalizations of Connes' non-commutative spin geometry encompassing non-commutative Riemannian, symplectic, complex-Hermitian and (Hyper-)Kaehler geometry. A general framework for non-commutative geometry is developed from the point of view of supersymmetry and illustrated in terms of examples. In particular, the non-commutative torus and the non-commutative 3-sphere are studied in some detail.
Cite
@article{arxiv.math-ph/9807006,
title = {Supersymmetric quantum theory and non-commutative geometry},
author = {J. Froehlich and O. Grandjean and A. Recknagel},
journal= {arXiv preprint arXiv:math-ph/9807006},
year = {2011}
}
Comments
77 pages, PlainTeX, no figures; present paper is a significantly extended version of the second half of hep-th/9612205. Assumptions in Sect. 2.2.5 clarified; final version to appear in Commun.Math.Phys