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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.15287 |
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| _version_ | 1866909028554113024 |
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| author | Frabetti, Alessandra Kravchenko, Olga Ryvkin, Leonid |
| author_facet | Frabetti, Alessandra Kravchenko, Olga Ryvkin, Leonid |
| contents | In this paper we construct a Poisson algebra bundle whose distributional sections are suitable to represent multilocal observables in classical field theory. To do this, we work with vector bundles over the unordered configuration space of a manifold $M$ and consider the structure of a $2$-monoidal category given by the usual (Hadamard) tensor product of bundles and a new (Cauchy) tensor product which provides a symmetrized version of the usual external tensor product of vector bundles on $M$. We use the symmetric algebras with respect to both products to obtain a Poisson 2-algebra bundle mimicking the construction of Peierls bracket from the causal propagator in field theory. The explicit description of observables from this Poisson algebra bundle will be carried out in a forthcoming paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15287 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Poisson bundles over unordered configurations Frabetti, Alessandra Kravchenko, Olga Ryvkin, Leonid Mathematical Physics Differential Geometry Rings and Algebras 17B63 (Primary), 18N10, 14D21, 70S99 (Secondary) In this paper we construct a Poisson algebra bundle whose distributional sections are suitable to represent multilocal observables in classical field theory. To do this, we work with vector bundles over the unordered configuration space of a manifold $M$ and consider the structure of a $2$-monoidal category given by the usual (Hadamard) tensor product of bundles and a new (Cauchy) tensor product which provides a symmetrized version of the usual external tensor product of vector bundles on $M$. We use the symmetric algebras with respect to both products to obtain a Poisson 2-algebra bundle mimicking the construction of Peierls bracket from the causal propagator in field theory. The explicit description of observables from this Poisson algebra bundle will be carried out in a forthcoming paper. |
| title | Poisson bundles over unordered configurations |
| topic | Mathematical Physics Differential Geometry Rings and Algebras 17B63 (Primary), 18N10, 14D21, 70S99 (Secondary) |
| url | https://arxiv.org/abs/2407.15287 |