The Hamilton-Pontryagin principle and multi-Dirac structures for classical field theories

J. Vankerschaver*, H. Yoshimura, M. Leok

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


We introduce a variational principle for field theories, referred to as the Hamilton-Pontryagin principlewe show that the resulting field equations are the Euler-Lagrange equations in implicit form. Second, we introduce multi-Dirac structures as a graded analog of standard Dirac structureswe show that the graph of a multisymplectic form determines a multi-Dirac structure. We then discuss the role of multi-Dirac structures in field theory by showing that the implicit Euler-Lagrange equations for fields obtained from the Hamilton-Pontryagin principle can be described intrinsically using multi-Dirac structures. Finally, we show a number of illustrative examples, including time-dependent mechanics, nonlinear scalar fields, Maxwell's equationselastostatics.

Original languageEnglish
Article number072903
JournalJournal of Mathematical Physics
Issue number7
Publication statusPublished - 2012 Jul 12

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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