A connection between massive electrodynamics and the Einstein-Maxwell equations

What is it about?

Quaternions are a suitable description of gauge-invariant massive electrodynamics. A comparable mass emerges when electrodynamics is described in curved space. In the Proca theory, photons are massive, but the dynamics causes gauge symmetry to be broken.

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Why is it important?

Anytime electromagnetic equations are stated in quaternionic or curved space, massive electrodynamics emerges. The mass of photons is brought about by the shared noncommutative structure of quaternions, which are curvatures. Photons have no mass in the standard model. Therefore, massless photons are a mathematical challenge rather than a physical one.