2002/12/11 by Frédéric Hélein, Frederic Helein, Helein, Frederic
Mathematics · Physics and Astronomy · #53C80 #53D99 #58E30 #81T99 #Advanced Topics in Algebra #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #math-ph #math.AP #math.MP #msc:53C80 #msc:53D99 #msc:58E30 #msc:81T99
paper · pdf · doi:10.48550/arxiv.math-ph/0212036
24 pages, conference in the honour of H. Brezis and F. Browder, Rutgers University, October 2001
arxiv created 2002/12/11 · openalex publication_date 2002/12/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.