Gunther's formalism (k-symplectic formalism) in classical field theory: Skinner-Rusk approach and the evolution operator

TL;DR

This paper extends the Skinner-Rusk formalism and the evolution operator to first-order classical field theories within Gunther's k-symplectic framework, providing a unified geometric approach.

Contribution

It generalizes Skinner-Rusk formalism and the evolution operator to classical field theories using k-symplectic geometry, bridging a gap in geometric formulations.

Findings

Extended Skinner-Rusk formalism to field theories.

Generalized the evolution K-operator in k-symplectic formalism.

Provided a geometric framework for classical field theories.

Abstract

The first aim of this paper is to extend the Skinner-Rusk formalism on classical mechanics for first-order field theories. The second is to generalize the definition and properties of the evolution K-operator on classical mechanics for first-order field theories using in both cases Gunther's formalism (k-symplectic formalism).