Non-existence of natural states for Abelian Chern-Simons theory
  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. 
Claudio Dappiaggi, Simone Murro, Alexander Schenkel
math-ph hep-th math.MP