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Poisson algebras for non-linear field theories in the Cahiers topos

Benini, Marco; Schenkel, Alexander

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Authors

Marco Benini



Abstract

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.

Citation

Benini, M., & Schenkel, A. (2017). Poisson algebras for non-linear field theories in the Cahiers topos. Annales Henri Poincaré, 18(4), 1435-1464. https://doi.org/10.1007/s00023-016-0533-2

Journal Article Type Article
Acceptance Date Oct 3, 2016
Online Publication Date Nov 17, 2016
Publication Date Apr 1, 2017
Deposit Date Mar 6, 2017
Publicly Available Date Mar 6, 2017
Journal Annales Henri Poincaré
Print ISSN 1424-0637
Electronic ISSN 1424-0661
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 18
Issue 4
Pages 1435-1464
DOI https://doi.org/10.1007/s00023-016-0533-2
Keywords non-linear classical field theory, synthetic differential geometry, Cahiers topos, Poisson algebras
Public URL https://nottingham-repository.worktribe.com/output/828058
Publisher URL http://link.springer.com/article/10.1007%2Fs00023-016-0533-2
Related Public URLs https://arxiv.org/abs/1602.00708
Additional Information The final publication is available at Springer via http://dx.doi.org/10.1007/s00023-016-0533-2.
Contract Date Mar 6, 2017

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