dorsal/arxiv
View SchemaPoisson brackets with divergence terms in field theories: two examples
| Authors | L. A. Dickey |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9703001 |
| URL | https://arxiv.org/abs/solv-int/9703001 |
Abstract
In field theories one often works with the functionals which are integrals of some densities. These densities are defined up to divergence terms (boundary terms). A Poisson bracket of two functionals is also a functional, i.e., an integral of a density. Suppose the divergence term in the density of the Poisson bracket be fixed so that it becomes a bilinear form of densities of two functionals. Then the left-hand side of the Jacobi identity written in terms of densities is not necessarily zero but a divergence of a trilinear form. The question is: what can be said about this trilinear form, what kind of a higher Jacobi identity (involving four fields) it enjoys? Two examples whose origin is the theory of integrable systems are given.
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"abstract": "In field theories one often works with the functionals which are integrals of\nsome densities. These densities are defined up to divergence terms (boundary\nterms). A Poisson bracket of two functionals is also a functional, i.e., an\nintegral of a density. Suppose the divergence term in the density of the\nPoisson bracket be fixed so that it becomes a bilinear form of densities of two\nfunctionals. Then the left-hand side of the Jacobi identity written in terms of\ndensities is not necessarily zero but a divergence of a trilinear form. The\nquestion is: what can be said about this trilinear form, what kind of a higher\nJacobi identity (involving four fields) it enjoys? Two examples whose origin is\nthe theory of integrable systems are given.",
"arxiv_id": "solv-int/9703001",
"authors": [
"L. A. Dickey"
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"title": "Poisson brackets with divergence terms in field theories: two examples",
"url": "https://arxiv.org/abs/solv-int/9703001"
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