# 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.

Keywords:

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