De Donder-Weyl Equations and Multisymplectic Geometry
arXiv:math-ph/0107019 · doi:10.1016/S0034-4877(02)80030-1
Abstract
Multisymplectic geometry is an adequate formalism to geometrically describe first order classical field theories. The De Donder-Weyl equations are treated in the framework of multisymplectic geometry, solutions are identified as integral manifolds of Hamiltonean multivectorfields. In contrast to mechanics, solutions cannot be described by points in the multisymplectic phase space. Foliations of the configuration space by solutions and a multisymplectic version of Hamilton-Jacobi theory are also discussed.
Talk given by H. Roemer at the 33rd Symposium on Mathematical Physics, Torun, Poland, June 2001