On the equivalence of AQFTs and prefactorization algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915756840583168 |
|---|---|
| author | Benini, Marco Carmona, Victor Grant-Stuart, Alastair Schenkel, Alexander |
| author_facet | Benini, Marco Carmona, Victor Grant-Stuart, Alastair Schenkel, Alexander |
| contents | This paper revisits the equivalence problem between algebraic quantum field theories and prefactorization algebras defined over globally hyperbolic Lorentzian manifolds. We develop a radically new approach whose main innovative features are 1.) a structural implementation of the additivity property used in earlier approaches and 2.) a reduction of the global equivalence problem to a family of simpler spacetime-wise problems. When applied to the case where the target category is a symmetric monoidal $1$-category, this yields a generalization of the equivalence theorem from [Commun. Math. Phys. 377, 971 (2019)]. In the case where the target is the symmetric monoidal $\infty$-category of cochain complexes, we obtain a reduction of the global $\infty$-categorical equivalence problem to simpler, but still challenging, spacetime-wise problems. The latter would be solved by showing that certain functors between $1$-categories exhibit $\infty$-localizations, however the available detection criteria are inconclusive in our case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07318 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the equivalence of AQFTs and prefactorization algebras Benini, Marco Carmona, Victor Grant-Stuart, Alastair Schenkel, Alexander Mathematical Physics High Energy Physics - Theory Algebraic Topology Quantum Algebra 81Txx, 18Nxx, 53C50 This paper revisits the equivalence problem between algebraic quantum field theories and prefactorization algebras defined over globally hyperbolic Lorentzian manifolds. We develop a radically new approach whose main innovative features are 1.) a structural implementation of the additivity property used in earlier approaches and 2.) a reduction of the global equivalence problem to a family of simpler spacetime-wise problems. When applied to the case where the target category is a symmetric monoidal $1$-category, this yields a generalization of the equivalence theorem from [Commun. Math. Phys. 377, 971 (2019)]. In the case where the target is the symmetric monoidal $\infty$-category of cochain complexes, we obtain a reduction of the global $\infty$-categorical equivalence problem to simpler, but still challenging, spacetime-wise problems. The latter would be solved by showing that certain functors between $1$-categories exhibit $\infty$-localizations, however the available detection criteria are inconclusive in our case. |
| title | On the equivalence of AQFTs and prefactorization algebras |
| topic | Mathematical Physics High Energy Physics - Theory Algebraic Topology Quantum Algebra 81Txx, 18Nxx, 53C50 |
| url | https://arxiv.org/abs/2412.07318 |