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

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.

arXiv commentv2: 7 pages; Final version published in Journal of Geometry and Physics

References in corpus (3)

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• Dynamical locality and covariance: What makes a physical theory the same in all spacetimes?
• A C*-algebra for quantized principal U(1)-connections on globally hyperbolic Lorentzian manifolds

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• The linear CS/WZW bulk/boundary system in AQFT
• On the uniqueness of invariant states