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Relativistic observer and Maxwell equations

The Ehresmann connection on a fiber bundle that is not compatible with a (possible) Lie group structure is illustrated by the geometry of a general anholonomic observer in the Minkowski space. The 3D split of Maxwell's equations induces geometric terms that are the (generalized) curvature and torque of the connection. The notion of torque is introduced here as a Lie coalgebra-valued endomorphism field and measures the deviation of a connection from being principal.