Differential Calculus on Fuzzy Sphere and Scalar Field
q-alg
2009-10-30 v1 Quantum Algebra
Abstract
We find that there is an alternative possibility to define the chirality operator on the fuzzy sphere, due to the ambiguity of the operator ordering. Adopting this new chirality operator and the corresponding Dirac operator, we define Connes' spectral triple on the fuzzy sphere and the differential calculus. The differential calculus based on this new spectral triple is simplified considerably. Using this formulation the action of the scalar field is derived.
Cite
@article{arxiv.q-alg/9710034,
title = {Differential Calculus on Fuzzy Sphere and Scalar Field},
author = {Ursula Carow-Watamura and Satoshi Watamura},
journal= {arXiv preprint arXiv:q-alg/9710034},
year = {2009}
}
Comments
LaTeX 12 pages