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Multisymplectic Lagrangian and Hamiltonian formalisms of classical field theories
Román Roy, Narciso
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions
This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler–Lagrange and the Hamilton–De Donder–Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems.
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial
Field theory (Physics)
Lagrange equations
Fiber bundles (Mathematics)
Camps, Teoria dels (Física)
Lagrange, Equacions de
Topologia algebraica
Classificació AMS::70 Mechanics of particles and systems::70S Classical field theories
Classificació AMS::55 Algebraic topology::55R Fiber spaces and bundles
Classificació AMS::53 Differential geometry::53C Global differential geometry
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/publishedVersion
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