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.
Original language | English |
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Article number | 16 |
Pages (from-to) | 1-43 |
Number of pages | 43 |
Journal | Letters in Mathematical Physics |
Volume | 115 |
Issue number | 1 |
Early online date | 3 Feb 2025 |
DOIs | |
Publication status | E-pub ahead of print - 3 Feb 2025 |
Keywords
- 18N10
- 53C50
- 81Txx
- Algebraic quantum field theory
- Bordisms
- Functorial field theory
- Lorentzian geometry
- Pseudo-categories