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A gauge-theoretic description of $μ$-prolongations, and $μ$-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 $μ$-prolongation of vector fields (which generalizes the $\la$-prolongation of Muriel and Romero), and hence $μ$-symmetries of differential equations, arise naturally. This is turn suggests several directions for further development. S0ome detailed examples are also given.