descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2020Embargo end date: 01 Jan 2018 English Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Journal of Geometric Mechanics, volume 12, pages 1-23 (issn: 1941-4897,

Authors: Gràcia Sabaté, Francesc Xavier; Rivas Guijarro, Xavier; Román Roy, Narciso;

doi: 10.3934/jgm.2020002 , 10.48550/arxiv.1812.08487

arXiv: http://arxiv.org/abs/1812.08487

handle: 2117/176508

Constraint algorithm for singular field theories in the <i>k</i>-cosymplectic framework

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Abstract

The aim of this paper is to develop a constraint algorithm for singular classical field theories in the framework of $k$-cosymplectic geometry. Since these field theories are singular, we need to introduce the notion of $k$-precosymplectic structure, which is a generalization of the $k$-cosymplectic structure. Next $k$-precosymplectic Hamiltonian systems are introduced in order to describe singular field theories, both in Lagrangian and Hamiltonian formalisms. Finally, we develop a constraint algorithm in order to find a submanifold where the existence of solutions of the field equations is ensured. The case of affine Lagrangians is studied as a relevant example.

24 pp. Some errors corrected in Section 6.1. The example in Section 6.2 has been changed. Acknowledgements updated

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High Energy Physics - Theory, singular field theories, Camps, Classificació AMS::53 Differential geometry::53D Symplectic geometry, :Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC], Geometria simplèctica, Statics, Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry, Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics, affine Lagrangian, Hamilton, Classificació AMS::35 Partial differential equations::35R Miscellaneous topics involving partial differential equations, Classificació AMS::70 Mechanics of particles and systems::70S Classical field theories, Mathematical Physics, Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial, Hamiltonian formalism, Symplectic geometry, Mathematical Physics (math-ph), Differential equations, Partial, :53 Differential geometry::53C Global differential geometry [Classificació AMS], Sistemes de, Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra, Partial, Differential equations, Field theory (Physics), Classificació AMS::53 Differential geometry::53C Global differential geometry, Geometria diferencial, FOS: Physical sciences, :35 Partial differential equations::35R Miscellaneous topics involving partial differential equations [Classificació AMS], Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions diferencials ordinàries, :Matemàtiques i estadística::Equacions diferencials i integrals::Equacions diferencials ordinàries [Àrees temàtiques de la UPC], Primary: 70H45, Secondary: 35R01, 53C15, 53D99, 70G45, 70S05, contact geometry, k-cosymplectic manifold, Lagrangian formalism, :70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics [Classificació AMS], :70 Mechanics of particles and systems::70S Classical field theories [Classificació AMS], Differential geometry, :Matemàtiques i estadística::Geometria::Geometria diferencial [Àrees temàtiques de la UPC], Hamiltonian systems, Camps, Teoria dels (Física), Estàtica, Classificació AMS::70 Mechanics of particles and systems::70C20 Statics, Equacions en derivades parcials, k-precosymplectic manifold, :Matemàtiques i estadística::Àlgebra [Àrees temàtiques de la UPC], :53 Differential geometry::53D Symplectic geometry, contact geometry [Classificació AMS], constraint algo- rithm, :70 Mechanics of particles and systems::70C20 Statics [Classificació AMS], High Energy Physics - Theory (hep-th), Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, Hamilton, Sistemes de, Teoria dels (Física)

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Constraint algorithm for singular k-cosymplectic field theories
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