Poisson algebras for non-linear field theories in the Cahiers topos
We develop an approach to construct Poisson algebras for non-linear scalar field theories that is based on the Cahiers topos model for synthetic differential geometry. In this framework the solution space of the field equation carries a natural smooth structure and, following Zuckerman's ideas,...
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| Format: | Article |
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Springer Verlag
2016
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| Online Access: | https://eprints.nottingham.ac.uk/41000/ |
| _version_ | 1848796174941683712 |
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| author | Benini, Marco Schenkel, Alexander |
| author_facet | Benini, Marco Schenkel, Alexander |
| author_sort | Benini, Marco |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We develop an approach to construct Poisson algebras for non-linear scalar field theories that is based on the Cahiers topos model for synthetic differential geometry. In this framework the solution space of the field equation carries a natural smooth structure and, following Zuckerman's ideas, we can endow it with a presymplectic current. We formulate the Hamiltonian vector field equation in this setting and show that it selects a family of observables which forms a Poisson algebra. Our approach provides a clean splitting between geometric and algebraic aspects of the construction of a Poisson algebra, which are sufficient to guarantee existence, and analytical aspects that are crucial to analyze its properties. |
| first_indexed | 2025-11-14T19:43:48Z |
| format | Article |
| id | nottingham-41000 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:48Z |
| publishDate | 2016 |
| publisher | Springer Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-410002020-05-04T18:20:41Z https://eprints.nottingham.ac.uk/41000/ Poisson algebras for non-linear field theories in the Cahiers topos Benini, Marco Schenkel, Alexander We develop an approach to construct Poisson algebras for non-linear scalar field theories that is based on the Cahiers topos model for synthetic differential geometry. In this framework the solution space of the field equation carries a natural smooth structure and, following Zuckerman's ideas, we can endow it with a presymplectic current. We formulate the Hamiltonian vector field equation in this setting and show that it selects a family of observables which forms a Poisson algebra. Our approach provides a clean splitting between geometric and algebraic aspects of the construction of a Poisson algebra, which are sufficient to guarantee existence, and analytical aspects that are crucial to analyze its properties. Springer Verlag 2016-11-17 Article PeerReviewed Benini, Marco and Schenkel, Alexander (2016) Poisson algebras for non-linear field theories in the Cahiers topos. Annales Henri Poincaré . pp. 1-30. ISSN 1424-0661 non-linear classical field theory synthetic differential geometry Cahiers topos Poisson algebras http://link.springer.com/article/10.1007%2Fs00023-016-0533-2 doi:10.1007/s00023-016-0533-2 doi:10.1007/s00023-016-0533-2 |
| spellingShingle | non-linear classical field theory synthetic differential geometry Cahiers topos Poisson algebras Benini, Marco Schenkel, Alexander Poisson algebras for non-linear field theories in the Cahiers topos |
| title | Poisson algebras for non-linear field theories in the Cahiers topos |
| title_full | Poisson algebras for non-linear field theories in the Cahiers topos |
| title_fullStr | Poisson algebras for non-linear field theories in the Cahiers topos |
| title_full_unstemmed | Poisson algebras for non-linear field theories in the Cahiers topos |
| title_short | Poisson algebras for non-linear field theories in the Cahiers topos |
| title_sort | poisson algebras for non-linear field theories in the cahiers topos |
| topic | non-linear classical field theory synthetic differential geometry Cahiers topos Poisson algebras |
| url | https://eprints.nottingham.ac.uk/41000/ https://eprints.nottingham.ac.uk/41000/ https://eprints.nottingham.ac.uk/41000/ |