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- W4300082714 abstract "The purpose of this paper is to define the concept of multi-Dirac structures and to describe their role in the description of classical field theories. We begin by outlining a variational principle for field theories, referred to as the Hamilton-Pontryagin principle, and we show that the resulting field equations are the Euler-Lagrange equations in implicit form. Secondly, we introduce multi-Dirac structures as a graded analog of standard Dirac structures, and we 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 field equations obtained from the Hamilton-Pontryagin principle can be described intrinsically using multi-Dirac structures. Furthermore, we show that any multi-Dirac structure naturally gives rise to a multi-Poisson bracket. We treat the case of field theories with nonholonomic constraints, showing that the integrability of the constraints is equivalent to the integrability of the underlying multi-Dirac structure. We finish with a number of illustrative examples, including time-dependent mechanics, nonlinear scalar fields and the electromagnetic field." @default.
- W4300082714 created "2022-10-03" @default.
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- W4300082714 date "2010-08-02" @default.
- W4300082714 modified "2023-09-28" @default.
- W4300082714 title "Multi-Dirac Structures and Hamilton-Pontryagin Principles for Lagrange-Dirac Field Theories" @default.
- W4300082714 doi "https://doi.org/10.48550/arxiv.1008.0252" @default.
- W4300082714 hasPublicationYear "2010" @default.
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