Classical Fields
The classical fields E and B together make up the antisymmetric tensor, . Introduce three new fields, e and b which have EM counterparts, and a 4vector field g^{u} for the diagonal components of the
symmetric tensor,
.
 Electric field.

Symmetric analog to E field.

Magnetic field.

Symmetric analog to the B field.

Diagonal of .
3+3+4+3+3=16 fields total.