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2 results on '"35Q99, 53D99, 55R10, 70H45, 70S05"'

1. Constraint algorithm for k-presymplectic Hamiltonian systems. Application to singular field theories

Author

Gracia, Xavier, Martin, Ruben, and Roman-Roy, Narciso

Subjects
Mathematical Physics, 35Q99, 53D99, 55R10, 70H45, 70S05
Abstract

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 algorithm that can be applied to $k$-presymplectic field theory, and more particularly to the Lagrangian and Hamiltonian formulations of field 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., Comment: 22 pp

Published
2009
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2. Constraint algorithm for k-presymplectic hamiltonian systems: application to singular field theories

Author

Narciso Román-Roy, Xavier Gràcia, Rubén Martín, Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV, and Universitat Politècnica de Catalunya. DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions

Subjects
Field theory (Physics), Physics and Astronomy (miscellaneous), Geometria diferencial, FOS: Physical sciences, Feixos fibrats (Matemàtica), Lagrange, Funcions de, Equacions diferencials, Hamiltonian system, Lagrangian and Hamiltonian formalisms, symbols.namesake, Constraint algorithm, 70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics [Classificació AMS], Applied mathematics, Trigonometric functions, 70 Mechanics of particles and systems::70S Classical field theories [Classificació AMS], Differential geometry, Camps, Teoria dels (Física), Mathematics::Symplectic Geometry, Mathematical Physics, Feld theories, Mathematics, 35 Partial differential equations::35Q Equations of mathematical physics and other areas of application [Classificació AMS], k-symplectic and k-presymplectic manifolds, Tangent, Matemàtiques i estadística [Àrees temàtiques de la UPC], Mathematical Physics (math-ph), 35Q99, 53D99, 55R10, 70H45, 70S05, Espais fibrats (Matemàtica), 53 Differential geometry::53D Symplectic geometry, contact geometry [Classificació AMS], Partial differential equations, 55 Algebraic topology::55R Fiber spaces and bundles [Classificació AMS], Formalism (philosophy of mathematics), Close relationship, Lagrangian functions, symbols, Fiber spaces (Mathematics), Lagrangian, Symplectic geometry
Abstract

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 algorithm that can be applied to $k$-presymplectic field theory, and more particularly to the Lagrangian and Hamiltonian formulations of field 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., Comment: 22 pp

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