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.

• Journal Article Type: Article
• Acceptance Date: Jan 13, 2017
• Online Publication Date: Feb 6, 2017
• Publication Date: 2017-06
• Deposit Date: Mar 2, 2017
• Publicly Available Date: Mar 2, 2017
• Journal: Journal of Geometry and Physics
• Print ISSN: 0393-0440
• Electronic ISSN: 0393-0440
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 116
• Pages: 119-123
• DOI: https://doi.org/10.1016/j.geomphys.2017.01.015
• Keywords: Locally covariant quantum field theory; Natural states; Chern–Simons theory; Gauge theory
• Public URL: https://nottingham-repository.worktribe.com/output/870295
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0393044017300281
• Related Public URLs: https://arxiv.org/abs/1612.04080
• Additional Information: This article is maintained by: Elsevier; Article Title: Non-existence of natural states for Abelian Chern–Simons theory; Journal Title: Journal of Geometry and Physics; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.geomphys.2017.01.015; Content Type: article; Copyright: © 2017 Elsevier B.V. All rights reserved.