Designing the sound of a cut-off drum
Abstract
The spectral action in noncommutative geometry naturally implements an ultraviolet cut-off, by counting the eigenvalues of a (generalized) Dirac operator lower than an energy of unification. Inverting the well known question "how to hear the shape of a drum ?", we ask what drum can be designed by hearing the truncated music of the spectral action ? This makes sense because the same Dirac operator also determines the metric, via Connes distance. The latter thus offers an original way to implement the high-momentum cut-off of the spectral action as a short distance cut-off on space. This is a non-technical presentation of the results of arXiv:1305.2605
Keywords
Cite
@article{arxiv.1502.02720,
title = {Designing the sound of a cut-off drum},
author = {Pierre Martinetti},
journal= {arXiv preprint arXiv:1502.02720},
year = {2015}
}
Comments
Published version in the Proceedings of the conference "Frontiers of Fundamental Physics 14" - FFP14, 15-18 July 2014, Aix Marseille University (AMU) Saint-Charles Campus, Marseille. Typos corrected, one reference added