Günther’s formalism (k-symplectic formalism) in classical field theory: Skinner–Rusk approach and the evolution operator

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 Günther’s formalism (k-symplectic formalism).