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

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

2004-01-28

arxiv.org/abs/math-ph/0401046v1

Physics

Mathematical Physics

31 pages, 2 figures

Scientific paper

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).

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