Covariant Hamiltonian formalism for the calculus of variations with several variables: Lepage--Dedecker versus de Donder--Weyl

Frederic Helein; Joseph Kouneiher

RECORD

Covariant Hamiltonian formalism for the calculus of variations with several variables: Lepage--Dedecker versus de Donder--Weyl

Frederic Helein, Joseph Kouneiher

Mathematical Physics · Submitted 28 Jan 2004

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

The authors' main claim One of the main points is the fact that the Legendre transform in the dDW approach is replaced by a Legendre correspondence in the LP theory (This correspondence behaves differently: ignoring the singularities whenever the Lagrangian is degenerate).

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDmath-ph/0401046 (version 1)

Pith ID4X3UL7CO, Pith's permanent record of this paper and its review

CitationFrederic Helein, Joseph Kouneiher. "Covariant Hamiltonian formalism for the calculus of variations with several variables: Lepage--Dedecker versus de Donder--Weyl." arXiv:math-ph/0401046 (2004). https://pith.science/paper/4X3UL7CO

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,086 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.45 · human participants 0.02 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.88 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

The main purpose in the present paper is to build a Hamiltonian theory for fields which is consistent with the principles of relativity. For this we consider detailed geometric pictures of Lepage theories in the spirit of Dedecker and try to stress out the interplay between the Lepage-Dedecker (LP) description and the (more usual) de Donder-Weyl (dDW) one. One of the main points is the fact that the Legendre transform in the dDW approach is replaced by a Legendre correspondence in the LP theory (This correspondence behaves differently: ignoring the singularities whenever the Lagrangian is degenerate).

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The main purpose in the present paper is to build a Hamiltonian theory for fields which is consistent with the principles of relativity.	contribution 0.93	0.47	0.10	asserted 0.95
s1	For this we consider detailed geometric pictures of Lepage theories in the spirit of Dedecker and try to stress out the interplay between the Lepage-Dedecker (LP) description and the (more usual) de Donder-Weyl (dDW) one.	method 0.63	0.75	0.07	asserted 0.76
s2	One of the main points is the fact that the Legendre transform in the dDW approach is replaced by a Legendre correspondence in the LP theory (This correspondence behaves differently: ignoring the singularities whenever the Lagrangian is degenerate).	result 0.54	0.45	0.32	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.79 · evidence from proof or derivation 0.81.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

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

The main purpose in the present paper is to build a Hamiltonian theory for fields which is consistent with the principles of relativity. For this we consider detailed geometric pictures of Lepage theories in the spirit of Dedecker and try to stress out the interplay between the Lepage-Dedecker (LP) description and the (more usual) de Donder-Weyl (dDW) one. One of the main points is the fact that the Legendre transform in the dDW approach is replaced by a Legendre correspondence in the LP theory (This correspondence behaves differently: ignoring the singularities whenever the Lagrangian is degenerate).

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

1 arXiv paper cite this in 16 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 11 sentences without a confident label

Uses its method or tool 1 paper

Following the method found in [ref] , we construct a bracket between the observable functionals $F [ω , Σ∩γ_ω ] := ∫_Σ∩γ_ω ω$ and $F [ϖ , Σ∩γ_ϖ ] := ∫_Σ∩γ_ϖ ϖ$, where $Σ$ is a $1$-codimensional slice [ref] , and $Σ∩γ_ω$ and $Σ∩γ_ϖ$ are submanifolds of codimension $n-2$ and $n-3$, respectively.

Multisymplectic formulation of vielbein gravity. De Donder-Weyl formulation, Hamiltonian (n-1)-forms · Towards the canonical forms for vielbein gravity · 0.99

Cites it as background 1 paper

Cariñena, Crampin and Ibort [ref] , Kanatchikov [ref] , Forger et al. [ref] , Hélein and Kouneiher [ref] .

Multisymplectic formulation of vielbein gravity. De Donder-Weyl formulation, Hamiltonian (n-1)-forms · Hamiltonian $(n-1)$-forms, homotopy Lie algebra · 0.95

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.