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$$F^{\mu\nu} = \begin{pmatrix}0 & -E_{x} & -E_{y} & -E_{z}\\

E_{x} & 0 & -B_{z} & B_{y}\\

E_{y} & B_{z} & 0 & -B_{x}\\

E_{z} & -B_{y} & B_{x} & 0

\end{pmatrix}$$

which is an anti-symmetric matrix. Recalling the one-to-one correspondence between skew-symmetric matrices and special orthogonal [rotation] matrices established by Cayley’s transformation, one could think of this tensor as an infinitesimal rotation matrix. As Lorentz boosts can also be interpreted as rotations, I wonder if those two concepts might be related in some way.

Could this correspondence have any physical interpretation? Does it make any sense at all to associate a general rotation of space-time coordinates with a given field? I'd welcome any thoughts/insights on this subject coming from any more knowledgeable person.