Hamiltonian formalisms for multidimensional calculus of variations and perturbation theory

Details Hamiltonian formalisms for multidimensional calculus of variations and perturbation theory Hamiltonian formalisms for multidimensional calculus of variations and perturbation theory

2002-12-11

arxiv.org/abs/math-ph/0212036v1

Physics

Mathematical Physics

24 pages, conference in the honour of H. Brezis and F. Browder, Rutgers University, October 2001

Scientific paper

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.

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