Algebraic quantum field theory on spacetimes with timelike boundary

Marco Benini, Claudio Dappiaggi, Alexander Schenkel
December 18, 2017
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.
open access link doi:10.1007/s00023-018-0687-1
@article{Benini:2017dfw, author = "Benini, Marco and Dappiaggi, Claudio and Schenkel, Alexander", title = "{Algebraic quantum field theory on spacetimes with timelike boundary}", journal = "Annales Henri Poincare", volume = "19", year = "2018", number = "8", pages = "2401-2433", doi = "10.1007/s00023-018-0687-1", eprint = "1712.06686", archivePrefix = "arXiv", primaryClass = "math-ph", reportNumber = "ZMP-HH/17-31, Hamburger Beitraege zur Mathematik Nr. 714, ZMP-HH-17-31, HAMBURGER-BEITRAEGE-ZUR-MATHEMATIK-NR.-714", SLACcitation = "%%CITATION = ARXIV:1712.06686;%%" }

Keywords: 
algebraic quantum field theory, timelike boundaries