De Donder-Weyl Equations and Multisymplectic Geometry

Details De Donder-Weyl Equations and Multisymplectic Geometry De Donder-Weyl Equations and Multisymplectic Geometry

2001-07-20

arxiv.org/abs/math-ph/0107019v1

Rept.Math.Phys. 49 (2002) 325-334

Physics

Mathematical Physics

Talk given by H. Roemer at the 33rd Symposium on Mathematical Physics, Torun, Poland, June 2001

Scientific paper

10.1016/S0034-4877(02)80030-1

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.

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