A gauge-theoretic description of $\mu$-prolongations, and $\mu$-symmetries of differential equations

Abstract

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

34 pages; PDF file 326 K. To appear in JGP

References in corpus (4)

• Nonlocal aspects of $\lambda$-symmetries and ODEs reduction
• Local and nonlocal solvable structures in ODEs reduction
• Noether theorem for mu-symmetries
• Reduction of systems of first-order differential equations via Lambda-symmetries

Cited by in corpus (2)

• Symmetry and Lie-Frobenius reduction of differential equations
• On the Geometry of Twisted Symmetries: Gauging and Coverings