# Non-existence of natural states for Abelian Chern-Simons theory

December 13, 2016

We give an elementary proof that Abelian Chern-Simons theory, described as a
functor from oriented surfaces to C*-algebras, does not admit a natural state.
Non-existence of natural states is thus not only a phenomenon of quantum field
theories on Lorentzian manifolds, but also of topological quantum field
theories formulated in the algebraic approach.

open access link
doi:10.1016/j.geomphys.2017.01.015

@article{Dappiaggi:2016dzo,
author = "Dappiaggi, Claudio and Murro, Simone and Schenkel,
Alexander",
title = "{Non-existence of natural states for Abelian Chern-Simons
theory}",
journal = "J. Geom. Phys.",
volume = "116",
year = "2017",
pages = "119-123",
doi = "10.1016/j.geomphys.2017.01.015",
eprint = "1612.04080",
archivePrefix = "arXiv",
primaryClass = "math-ph",
SLACcitation = "%%CITATION = ARXIV:1612.04080;%%"
}

Keywords:

locally covariant quantum field theory, Chern-Simons theory, natural states