Hamiltonian formalisms for multidimensional calculus of variations and perturbation theory
Helein, Frederic
arXiv, 0212036 / Harvested from arXiv
Text on arXiv
In a first part we propose an introduction to multisymplectic formalisms, which are generalisations of Hamilton's formulation of Mechanics to the calculus of variations with several variables: we give some physical motivations, related to the quantum field theory, and expound the simplest example, based on a theory due to T. de Donder and H. Weyl. In a second part we explain quickly a work in collaboration with J. Kouneiher (math-ph/0211046) on generalizations of the de Donder--Weyl theory (known as Lepage theories). Lastly we show that in this framework a perturbative classical field theory (analog of the perturbative quantum field theory) can be constructed.
Publié le : 2002-12-11
Classification:  Mathematical Physics,  Mathematics - Analysis of PDEs,  58E30,  53D99,  53C80,  81T99 
@article{0212036,
     author = {Helein, Frederic},
     title = {Hamiltonian formalisms for multidimensional calculus of variations and
  perturbation theory},
     journal = {arXiv},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0212036}
}

Helein, Frederic. Hamiltonian formalisms for multidimensional calculus of variations and
  perturbation theory. arXiv, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/0212036/