On the Multimomentum Bundles and the Legendre Maps in Field Theories

Abstract

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.

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

References in corpus (1)

• Fibre derivatives: some applications to singular lagrangians

Cited by in corpus (12)

• Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories
• Geometry of multisymplectic Hamiltonian first-order field theories
• Singular Lagrangian Systems on Jet Bundles
• Symmetries in Classical Field Theory
• Finite dimesional Hamiltonian formalism for gauge and field theories
• Precanonical Quantum Gravity: quantization without the space-time decomposition
• Geometric (pre)quantization in the polysymplectic approach to field theory
• Classical field theories of first order and lagrangian submanifolds of premultisymplectic manifolds
• Multisymplectic Theory of Balance Systems and Entropy Principle
• A new geometric setting for classical field theories
• Properties of Multisymplectic Manifolds
• Geometrical structures of higher-order dynamical systems and field theories