Abstract
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.
Highlights
Introduction and SummaryAlgebraic quantum field theory is a powerful and far developed framework to address model-independent aspects of quantum field theories on Minkowski spacetime [18] and more generally on globally hyperbolic spacetimes [7]
Experimental setups for studying the Casimir effect confine quantum field theories between several metal plates, which may be modeled theoretically by introducing timelike boundaries to the system. This immediately prompts the question whether the rigorous framework of algebraic quantum field theory admits a generalization to cover such scenarios
We strengthen this result in Theorem 5.10 by constructing an equivalence between the category of additive quantum field theories on M and a category of pairs (A, I) consisting of a theory A ∈ QFT(int M ) on the interior and an ideal I ⊆ ext A of the universal extension that is trivial on the interior
Summary
Notice that the results in Theorem 5.6 and Corollary 5.7 give the adjective universal a physical meaning in the sense that the extensions are sufficiently large such that any additive theory can be recovered by a quotient We strengthen this result in Theorem 5.10 by constructing an equivalence between the category of additive quantum field theories on M and a category of pairs (A, I) consisting of a theory A ∈ QFT(int M ) on the interior and an ideal I ⊆ ext A of the universal extension that is trivial on the interior. We included “Appendix A” to state some basic definitions and results of category theory which will be used in our work
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