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Communications in Mathematical Physics

, Volume 256, Issue 2, pp 375–410 | Cite as

Covariant Poisson Brackets in Geometric Field Theory

  • Michael ForgerEmail author
  • Sandro Vieira Romero
Article
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Abstract

We establish a link between the multisymplectic and the covariant phase space approach to geometric field theory by showing how to derive the symplectic form on the latter, as introduced by Crnković-Witten and Zuckerman, from the multisymplectic form. The main result is that the Poisson bracket associated with this symplectic structure, according to the standard rules, is precisely the covariant bracket due to Peierls and DeWitt.

Keywords

Neural Network Statistical Physic Field Theory Phase Space Complex System 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Departamento de Matemática Aplicada, Instituto de Matemática e EstatísticaUniversidade de São PauloSão PauloBrazil
  2. 2.Departamento de MatemáticaUniversidade Federal de ViçosaViçosaBrazil

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