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Lifted tensors and Hamilton-Jacobi separability

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G. Waeyaert, W. Sarlet

Differential Geometry · Submitted 18 Jul 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The integrability of these distributions, a coordinate free condition, is shown to produce exactly Forbat's conditions for separability of the time-dependent Hamilton-Jacobi equation in appropriate coordinates.

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arXiv ID1407.4968 (version 1)
Pith IDHZSQ27MA, Pith's permanent record of this paper and its review
CitationG. Waeyaert, W. Sarlet. "Lifted tensors and Hamilton-Jacobi separability." arXiv:1407.4968 (2014). https://pith.science/paper/HZSQ27MA
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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.50 · mentions code or data availability 0.01.

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Starting from a bundle E over R, the dual of the first jet bundle, which is a co-dimension 1 sub-bundle of the cotangent bundle of E, is the appropriate manifold for the geometric description of time-dependent Hamiltonian systems. Based on previous work, we recall properties of the complete lifts of a type (1,1) tensor R on E to both of these manifolds. We discuss how an interplay between these lifted tensors leads to the identification of related distributions on both manifolds. The integrability of these distributions, a coordinate free condition, is shown to produce exactly Forbat's conditions for separability of the time-dependent Hamilton-Jacobi equation in appropriate coordinates.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 Starting from a bundle E over R, the dual of the first jet bundle, which is a co-dimension 1 sub-bundle of the cotangent bundle of E, is the appropriate manifold for the geometric description of time-dependent Hamiltonian systems. background 1.00 0.13 0.04 asserted 1.00
s1 Based on previous work, we recall properties of the complete lifts of a type (1,1) tensor R on E to both of these manifolds. background 0.96 0.18 0.03 asserted 0.92
s2 We discuss how an interplay between these lifted tensors leads to the identification of related distributions on both manifolds. contribution 0.74 0.80 0.08 asserted 0.91
s3 The integrability of these distributions, a coordinate free condition, is shown to produce exactly Forbat's conditions for separability of the time-dependent Hamilton-Jacobi equation in appropriate coordinates. result 0.99 0.88 0.88 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Starting from a bundle E over R, the dual of the first jet bundle, which is a co-dimension 1 sub-bundle of the cotangent bundle of E, is the appropriate manifold for the geometric description of time-dependent Hamiltonian systems. Based on previous work, we recall properties of the complete lifts of a type (1,1) tensor R on E to both of these manifolds. We discuss how an interplay between these lifted tensors leads to the identification of related distributions on both manifolds. The integrability of these distributions, a coordinate free condition, is shown to produce exactly Forbat's conditions for separability of the time-dependent Hamilton-Jacobi equation in appropriate coordinates.

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