Lorentzian bordisms in algebraic quantum field theory
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916596013858816 |
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| author | Bunk, Severin MacManus, James Schenkel, Alexander |
| author_facet | Bunk, Severin MacManus, James Schenkel, Alexander |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_01026 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lorentzian bordisms in algebraic quantum field theory Bunk, Severin MacManus, James Schenkel, Alexander Mathematical Physics High Energy Physics - Theory Differential Geometry Quantum Algebra 81Txx, 18N10, 53C50 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. |
| title | Lorentzian bordisms in algebraic quantum field theory |
| topic | Mathematical Physics High Energy Physics - Theory Differential Geometry Quantum Algebra 81Txx, 18N10, 53C50 |
| url | https://arxiv.org/abs/2308.01026 |