Poisson Algebras for Non-Linear Field Theories in the Cahiers Topos

Marco Benini, Alexander Schenkel

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1435-1464
Number of pages30
JournalAnnales Henri Poincare
Volume18
Issue number4
Early online date17 Nov 2016
DOIs
Publication statusPublished - Apr 2017

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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