Constraint algorithm for singular field theories in the k-cosymplectic framework

Gràcia Xavier; Rivas Xavier; Román-Roy Narciso

doi:10.3934/jgm.2020002

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2020, Volume 12, Issue 1: 1-23. Doi: 10.3934/jgm.2020002

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Constraint algorithm for singular field theories in the k-cosymplectic framework

Department of Mathematics, Universitat Politècnica de Catalunya, Campus Nord UPC, edifici C3, C. Jordi Girona, 1, 08034 Barcelona, Catalonia, Spain

^* Corresponding author: Xavier Gràcia
^* Corresponding author: Xavier Gràcia

Received: December 31, 2018

Revised: June 30, 2019

Published: February 2020

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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.

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Mathematics Subject Classification: Primary: 70H45; Secondary: 35R01, 53C15, 53D99, 70G45, 70S05.

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