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arXiv · 1812.08487

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

Xavier Gràcia·Xavier Rivas·Narciso Román-Roy
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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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Xavier Gràcia, Xavier Rivas, Narciso Román-Roy. 2018-12-20. Constraint algorithm for singular field theories in the $k$-cosymplectic framework. https://doi.org/10.3934/jgm.2020002.

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