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

Dappiaggi, Claudio ; Murro, Simone ; Schenkel, Alexander



Abstract

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. (C) 2017 Elsevier B.V. All rights reserved.


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