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Lorentzian bordisms in algebraic quantum field theory

Bunk, Severin; MacManus, James; Schenkel, Alexander

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Authors

Severin Bunk

James MacManus



Abstract

It is shown that every algebraic quantum field theory has an underlying functorial field theory which is defined on a suitable globally hyperbolic Lorentzian bordism pseudo-category. This means that globally hyperbolic Lorentzian bordisms between Cauchy surfaces arise naturally in the context of algebraic quantum field theory. The underlying functorial field theory encodes the time evolution of the original theory, but not its spatially local structure. As an illustrative application of these results, the algebraic and functorial descriptions of a free scalar quantum field are compared in detail.

Citation

Bunk, S., MacManus, J., & Schenkel, A. (2025). Lorentzian bordisms in algebraic quantum field theory. Letters in Mathematical Physics, 115(1), Article 16. https://doi.org/10.1007/s11005-025-01906-3

Journal Article Type Article
Acceptance Date Jan 18, 2025
Online Publication Date Feb 3, 2025
Publication Date Feb 3, 2025
Deposit Date Feb 4, 2025
Publicly Available Date Feb 4, 2025
Journal Letters in Mathematical Physics
Print ISSN 0377-9017
Electronic ISSN 1573-0530
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 115
Issue 1
Article Number 16
DOI https://doi.org/10.1007/s11005-025-01906-3
Keywords Algebraic quantum field theory; Functorial field theory; Lorentzian geometry; Bordisms; Pseudo-categories
Public URL https://nottingham-repository.worktribe.com/output/45036692
Publisher URL https://link.springer.com/article/10.1007/s11005-025-01906-3

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