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

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

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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.

Item Type: Article
Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s00023-016-0533-2.
Keywords: non-linear classical field theory, synthetic differential geometry, Cahiers topos, Poisson algebras
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1007/s00023-016-0533-2
Depositing User: Schenkel, Dr Alexander
Date Deposited: 06 Mar 2017 08:43
Last Modified: 20 Mar 2017 07:03
URI: http://eprints.nottingham.ac.uk/id/eprint/41000

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