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

Claudio Dappiaggi, Simone Murro, Alexander Schenkel
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;%%" }

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