Noether Currents and Generators of Local Gauge Transformations in the Covariant Canonical Formalism

We investigate generators of local transformations in the covariant canonical formalism (CCF). The CCF treats space and time on an equal footing regarding differential forms as basic variables. conjugate $\pi_A$ are defined derivatives Lagrangian $d$-form $L(\psi^A, d\psi^A)$ with respect to $d\psi^A$, namely $\pi_A := \partial L/\partial d\psi^A$, where $\psi^A $ $p$-form dynamical fields. form-canonical equations derived from form-Legendre transformation form $H:=d\psi^A \wedge \pi_A - L$. show that Noether current is generator infinitesimal \to \psi^A + \delta \psi^A$ if given by $\delta L=dl$ $l$ depend only $\psi^A$ parameters. As instance, we study gauge for field Lorentz second order gravity.