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Constraint algorithm for k-presymplectic Hamiltonian systems. Application to singular field theories
Gràcia, Xavier; Martín Grillo, Rubén; Román Roy, Narciso
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
The k-symplectic formulation of field theories is especially simple, since only tangent and cotangent bundles are needed in its description. Its defining elements show a close relationship with those in the symplectic formulation of mechanics. It will be shown that this relationship also stands in the presymplectic case. In a natural way,one can mimick the presymplectic constraint algorithm to obtain a constraint algorithmthat can be applied to k-presymplectic field theory, and more particularly to the Lagrangian and Hamiltonian formulations offield theories defined by a singular Lagrangian, as well as to the unified Lagrangian-Hamiltonian formalism (Skinner--Rusk formalism) for k-presymplectic field theory. Two examples of application of the algorithm are also analyzed.
Àrees temàtiques de la UPC::Matemàtiques i estadística
Field theory
Hamiltonian systems
k-symplectic manifold
k-presymplectic manifold
Constraint algorithm
Field theories
Lagrangian formalism
Hamiltonian formalism
Sistemes dinàmics diferenciables
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Classificació AMS::70 Mechanics of particles and systems::70S Classical field theories
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