A complete classification of quadratic degenerate Maxwell-Einstein theories is given, including a new theory that generalizes Horndeski's non-minimal coupling to gauge fields.
Disformal invariance of Maxwell's field equations
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abstract
We show that Maxwell's electrodynamics in vacuum is invariant under active transformations of the metric. These metrics are related by disformal mappings induced by derivatives of the gauge vector $A_{\mu}$ such that the gauge symmetry is preserved. Our results generalize the well known conformal invariance of electrodynamics and characterize a new type of internal symmetry of the theory. The group structure associated with these transformations is also investigated in details.
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Degenerate higher-order Maxwell-Einstein theories
A complete classification of quadratic degenerate Maxwell-Einstein theories is given, including a new theory that generalizes Horndeski's non-minimal coupling to gauge fields.