Reduction of ∞-Algebras of Observables on Multisymplectic Manifolds
We develop a reduction scheme for the ∞-algebra of observables on a premultisymplectic manifold (, ) in the presence of a compatible Lie algebra action ↷ and a subset ⊂ . This reproduces in the symplectic setting the Poisson algebra of observables on the Marsden-Weinstein-Meyer symplectic reduced...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212359 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Reduction of ∞-Algebras of Observables on Multisymplectic Manifolds. Casey Blacker, Antonio Michele Miti and Leonid Ryvkin. SIGMA 20 (2024), 061, 47 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | We develop a reduction scheme for the ∞-algebra of observables on a premultisymplectic manifold (, ) in the presence of a compatible Lie algebra action ↷ and a subset ⊂ . This reproduces in the symplectic setting the Poisson algebra of observables on the Marsden-Weinstein-Meyer symplectic reduced space, whenever the reduced space exists, but is otherwise distinct from the Dirac, Śniatycki-Weinstein, and Arms-Cushman-Gotay observable reduction schemes. We examine various examples, including multicotangent bundles and multiphase spaces, and we conclude with a discussion of applications to classical field theories and quantization.
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| ISSN: | 1815-0659 |