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The Chern-Simons Function and the Quantum Hall Effect
Abstract
In this article, I will define the Chern-Simons invariant of a gauge connection over a three-manifold and explain some of the things that are special about it, in particular its role in understanding the quantum Hall effect, which is an important effect in condensed matter physics, and its generalization, the fractional quantum Hall effect. (The article is based on a lecture at a conference celebrating the 75th birthday of James Simons, held at the CUNY Graduate Center in 2013. It will appear in the Bulletin of the American Math Society.
Related
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BibTeX
@misc{witten2026chernsimons,
title = {{The Chern-Simons Function and the Quantum Hall Effect}},
author = {Edward Witten},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21182},
eprint = {2609.21182},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21182},
}
RIS
TY - UNPB
TI - The Chern-Simons Function and the Quantum Hall Effect
AU - Edward Witten
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.21182
UR - https://arxiv.org/abs/2609.21182
AB - In this article, I will define the Chern-Simons invariant of a gauge connection over a three-manifold and explain some of the things that are special about it, in particular its role in understanding the quantum Hall effect, which is an important effect in condensed matter physics, and its generalization, the fractional quantum Hall effect. (The article is based on a lecture at a conference celebrating the 75th birthday of James Simons, held at the CUNY Graduate Center in 2013. It will appear in the Bulletin of the American Math Society.
ER -