Annales Henri Poincaré

, Volume 19, Issue 8, pp 2401–2433 | Cite as

Algebraic Quantum Field Theory on Spacetimes with Timelike Boundary

  • Marco Benini
  • Claudio Dappiaggi
  • Alexander SchenkelEmail author
Open Access


We analyze quantum field theories on spacetimes M with timelike boundary from a model-independent perspective. We construct an adjunction which describes a universal extension to the whole spacetime M of theories defined only on the interior \(\mathrm {int}M\). The unit of this adjunction is a natural isomorphism, which implies that our universal extension satisfies Kay’s F-locality property. Our main result is the following characterization theorem: Every quantum field theory on M that is additive from the interior (i.e., generated by observables localized in the interior) admits a presentation by a quantum field theory on the interior \(\mathrm {int}M\) and an ideal of its universal extension that is trivial on the interior. We shall illustrate our constructions by applying them to the free Klein–Gordon field.


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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Fachbereich MathematikUniversität HamburgHamburgGermany
  2. 2.INFN, Sezione di PaviaUniversità di PaviaPaviaItaly
  3. 3.Dipartimento di FisicaINFN, Sezione di PaviaPaviaItaly
  4. 4.School of Mathematical SciencesUniversity of NottinghamNottinghamUK

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