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

TL;DR

This paper develops a constraint algorithm for k-presymplectic Hamiltonian systems, extending the presymplectic constraint algorithm to singular field theories within the k-symplectic framework, with practical applications demonstrated.

Contribution

It introduces a new constraint algorithm for k-presymplectic systems applicable to singular field theories, unifying Lagrangian and Hamiltonian formalisms.

Findings

Algorithm successfully applied to singular Lagrangian and Hamiltonian field theories.

Extended the presymplectic constraint algorithm to the k-symplectic setting.

Provided practical examples demonstrating the algorithm's effectiveness.

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.