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Boundary conditions in relativistic QFT can be classified by deep results in the theory of braided or modular tensor categories.
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M. Bischoff, Y. Kawahigashi, and R. Longo, Characterization of 2D rational local conformal nets and its boundary conditions: the maximal case, Documenta Math. 20
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M. Bischoff, Y. Kawahigashi, R. Longo, and K.-H. Rehren, Tensor categories and endomorphisms of von Neumann algebras, Springer Briefs in Math. Phys. 3
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2016
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