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

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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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Official URL: http://link.springer.com/article/10.1007%2Fs00023-016-0533-2

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

RIS ID:

https://nottingham-repository.worktribe.com/output/828058

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:

https://doi.org/10.1007/s00023-016-0533-2