An electromagnetic field is given by 6 components (Ex,Ey,Ez,Bx,By,Bz). Now this is a 6dimensional irreducible representation of so(1,3) which is a highest weight representation. So there should be a single function S(t,x,y,z) (a "superpotential") corresponding to the highest weight and such that all the other components are derived from it through lowering operators. A similar question can be asked for the electromagnetic 4potential, (\rho,Ax,Ay,Az); there should be a single function and lowering operators to derive all components. Can someone provide a reference where this is is discussed

The 6dimensional representation corresponding to the electromagnetic field is the realification of the symmetric square of the defining representation of $\mathrm{SL}(2,\mathbb{C})$, whose Lie algebra is isomorphic to that of $\mathrm{SO}(1,3)$. The highest weight vector is the square of the highest weight vector of the defining representation. Any book which treats electromagnetism in the "spinorial" language should discuss this: perhaps Penrose and Rindler "Spinors and spacetime"? 


I think I see the discrepancy. The 6 components of the field then do NOT transform as a 6 dimensional rep, even for a fixed spacetime point. The action is : F(x) > M(g) * F(g' x) (F=field, M : 6x6 matrix) which is an infinite dimensional rep. I don't see any finite reps here at all; so the common statement "the electromagnetic field transforms as a 6 dimensional rep..." really isn't true. That being said, is there any way to adapt the well structured theory of highest weight representation to this infinite representation.... 

