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arXiv · 2407.15287

Poisson bundles over unordered configurations

Alessandra Frabetti·Olga Kravchenko·Leonid Ryvkin
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Abstract

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.

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Alessandra Frabetti, Olga Kravchenko, Leonid Ryvkin. 2024-07-21. Poisson bundles over unordered configurations. https://arxiv.org/abs/2407.15287

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