A gauge-theoretic description of μμ-prolongations, and μμ-symmetries of differential equations

We consider generalized (possibly depending on fields as well as on space–time variables) gauge transformations and gauge symmetries in the context of general–that is, possibly non variational nor covariant–differential equations. In this case the relevant principal bundle admits the first jet bundle (of the phase manifold) as an associated bundle, at difference with standard Yang–Mills theories. We also show how in this context the recently introduced operation of μμ-prolongation of vector fields (which generalizes the λλ-prolongation of Muriel and Romero), and hence μμ-symmetries of differential equations, arise naturally. This is turn suggests several directions for further development.