Gluing algebraic quantum field theories on manifolds
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915095277207552 |
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| author | Anastopoulos, Angelos Benini, Marco |
| author_facet | Anastopoulos, Angelos Benini, Marco |
| contents | It has been observed that, given an algebraic quantum field theory (AQFT) on a manifold $M$ and an open cover $\{M_α\}$ of $M$, it is typically not possible to recover the global algebra of observables on $M$ by simply gluing the underlying local algebras subordinate to $\{M_α\}$. Instead of gluing local algebras, we introduce a gluing construction for AQFTs subordinate to $\{M_α\}$ and we show that for simple examples of AQFTs, constructed out of geometric data, gluing the local AQFTs subordinate to $\{M_α\}$ recovers the global AQFT on $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09638 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gluing algebraic quantum field theories on manifolds Anastopoulos, Angelos Benini, Marco Mathematical Physics Category Theory Quantum Algebra It has been observed that, given an algebraic quantum field theory (AQFT) on a manifold $M$ and an open cover $\{M_α\}$ of $M$, it is typically not possible to recover the global algebra of observables on $M$ by simply gluing the underlying local algebras subordinate to $\{M_α\}$. Instead of gluing local algebras, we introduce a gluing construction for AQFTs subordinate to $\{M_α\}$ and we show that for simple examples of AQFTs, constructed out of geometric data, gluing the local AQFTs subordinate to $\{M_α\}$ recovers the global AQFT on $M$. |
| title | Gluing algebraic quantum field theories on manifolds |
| topic | Mathematical Physics Category Theory Quantum Algebra |
| url | https://arxiv.org/abs/2404.09638 |