On the Multimomentum Bundles and the Legendre Maps in Field Theories

Details On the Multimomentum Bundles and the Legendre Maps in Field Theories On the Multimomentum Bundles and the Legendre Maps in Field Theories

1999-04-12

arxiv.org/abs/math-ph/9904007v2

Rept.Math.Phys. 45 (2000) 85-105

Physics

Mathematical Physics

LaTeX file, 19 pages. Replaced with the published version. Minor mistakes are corrected

Scientific paper

10.1016/S0034-4877(00)88873-4

We study the geometrical background of the Hamiltonian formalism of first-order Classical Field Theories. In particular, different proposals of multimomentum bundles existing in the usual literature (including their canonical structures) are analyzed and compared. The corresponding Legendre maps are introduced. As a consequence, the definition of regular and almost-regular Lagrangian systems is reviewed and extended from different but equivalent ways.

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